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Dreieck","Aussenwinkel berechnen","Außenwinkelsatz Dreieck","Außenwinkel gleich Summe der nicht anliegenden Innenwinkel",{"type":555,"value":556,"toc":2745},"minimark",[557,562,668,678,917,921,1196,1481,1485,1692,1924,2352,2420,2599,2603],[558,559,561],"h2",{"id":560},"erklärung","Erklärung",[563,564,565,566,570,571,667],"p",{},"Verlängert man eine Seite eines Dreiecks über eine Ecke hinaus, entsteht dort ein ",[567,568,569],"strong",{},"Außenwinkel",". Er ergänzt den Innenwinkel an dieser Ecke zu ",[572,573,576,606],"span",{"className":574},[575],"katex",[572,577,580],{"className":578},[579],"katex-mathml",[581,582,584],"math",{"xmlns":583},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[585,586,587,601],"semantics",{},[588,589,590],"mrow",{},[591,592,593,597],"msup",{},[594,595,596],"mn",{},"180",[598,599,600],"mo",{},"∘",[602,603,605],"annotation",{"encoding":604},"application\u002Fx-tex","180^\\circ",[572,607,611],{"className":608,"ariaHidden":610},[609],"katex-html","true",[572,612,615,620,625],{"className":613},[614],"base",[572,616],{"className":617,"style":619},[618],"strut","height:0.6741em;",[572,621,624],{"className":622},[623],"mord","18",[572,626,628,632],{"className":627},[623],[572,629,631],{"className":630},[623],"0",[572,633,636],{"className":634},[635],"msupsub",[572,637,640],{"className":638},[639],"vlist-t",[572,641,644],{"className":642},[643],"vlist-r",[572,645,648],{"className":646,"style":619},[647],"vlist",[572,649,651,656],{"style":650},"top:-3.063em;margin-right:0.05em;",[572,652],{"className":653,"style":655},[654],"pstrut","height:2.7em;",[572,657,663],{"className":658},[659,660,661,662],"sizing","reset-size6","size3","mtight",[572,664,600],{"className":665},[666,662],"mbin",", ist also sein Nebenwinkel.",[563,669,670,671,673,674,677],{},"Der ",[567,672,548],{}," sagt: Der Außenwinkel ist genauso groß wie die beiden Innenwinkel an den ",[567,675,676],{},"anderen"," zwei Ecken zusammen. Den Innenwinkel an derselben Ecke braucht man dafür nicht.",[563,679,680,681,808,809,916],{},"An jeder Ecke gilt das entsprechend: ",[572,682,684,719],{"className":683},[575],[572,685,687],{"className":686},[579],[581,688,689],{"xmlns":583},[585,690,691,716],{},[588,692,693,704,707,710,713],{},[591,694,695,699],{},[696,697,698],"mi",{},"β",[598,700,703],{"mathvariant":701,"lspace":702,"rspace":702},"normal","0em","′",[598,705,706],{},"=",[696,708,709],{},"α",[598,711,712],{},"+",[696,714,715],{},"γ",[602,717,718],{"encoding":604},"\\beta' = \\alpha + \\gamma",[572,720,722,776,797],{"className":721,"ariaHidden":610},[609],[572,723,725,729,764,769,773],{"className":724},[614],[572,726],{"className":727,"style":728},[618],"height:0.9463em;vertical-align:-0.1944em;",[572,730,732,737],{"className":731},[623],[572,733,698],{"className":734,"style":736},[623,735],"mathnormal","margin-right:0.0528em;",[572,738,740],{"className":739},[635],[572,741,743],{"className":742},[639],[572,744,746],{"className":745},[643],[572,747,750],{"className":748,"style":749},[647],"height:0.7519em;",[572,751,752,755],{"style":650},[572,753],{"className":754,"style":655},[654],[572,756,758],{"className":757},[659,660,661,662],[572,759,761],{"className":760},[623,662],[572,762,703],{"className":763},[623,662],[572,765],{"className":766,"style":768},[767],"mspace","margin-right:0.2778em;",[572,770,706],{"className":771},[772],"mrel",[572,774],{"className":775,"style":768},[767],[572,777,779,783,787,791,794],{"className":778},[614],[572,780],{"className":781,"style":782},[618],"height:0.6667em;vertical-align:-0.0833em;",[572,784,709],{"className":785,"style":786},[623,735],"margin-right:0.0037em;",[572,788],{"className":789,"style":790},[767],"margin-right:0.2222em;",[572,792,712],{"className":793},[666],[572,795],{"className":796,"style":790},[767],[572,798,800,804],{"className":799},[614],[572,801],{"className":802,"style":803},[618],"height:0.625em;vertical-align:-0.1944em;",[572,805,715],{"className":806,"style":807},[623,735],"margin-right:0.0556em;"," und ",[572,810,812,838],{"className":811},[575],[572,813,815],{"className":814},[579],[581,816,817],{"xmlns":583},[585,818,819,835],{},[588,820,821,827,829,831,833],{},[591,822,823,825],{},[696,824,715],{},[598,826,703],{"mathvariant":701,"lspace":702,"rspace":702},[598,828,706],{},[696,830,709],{},[598,832,712],{},[696,834,698],{},[602,836,837],{"encoding":604},"\\gamma' = \\alpha + \\beta",[572,839,841,888,906],{"className":840,"ariaHidden":610},[609],[572,842,844,847,879,882,885],{"className":843},[614],[572,845],{"className":846,"style":728},[618],[572,848,850,853],{"className":849},[623],[572,851,715],{"className":852,"style":807},[623,735],[572,854,856],{"className":855},[635],[572,857,859],{"className":858},[639],[572,860,862],{"className":861},[643],[572,863,865],{"className":864,"style":749},[647],[572,866,867,870],{"style":650},[572,868],{"className":869,"style":655},[654],[572,871,873],{"className":872},[659,660,661,662],[572,874,876],{"className":875},[623,662],[572,877,703],{"className":878},[623,662],[572,880],{"className":881,"style":768},[767],[572,883,706],{"className":884},[772],[572,886],{"className":887,"style":768},[767],[572,889,891,894,897,900,903],{"className":890},[614],[572,892],{"className":893,"style":782},[618],[572,895,709],{"className":896,"style":786},[623,735],[572,898],{"className":899,"style":790},[767],[572,901,712],{"className":902},[666],[572,904],{"className":905,"style":790},[767],[572,907,909,913],{"className":908},[614],[572,910],{"className":911,"style":912},[618],"height:0.8889em;vertical-align:-0.1944em;",[572,914,698],{"className":915,"style":736},[623,735],". Folgerung: Ein Außenwinkel ist immer größer als jeder der beiden nicht anliegenden Innenwinkel.",[558,918,920],{"id":919},"herleitung","Herleitung",[563,922,923,924,1066,1067,1195],{},"Der Außenwinkel und der Innenwinkel an derselben Ecke ergeben zusammen einen gestreckten Winkel: ",[572,925,927,958],{"className":926},[575],[572,928,930],{"className":929},[579],[581,931,932],{"xmlns":583},[585,933,934,955],{},[588,935,936,942,944,950,953],{},[591,937,938,940],{},[696,939,709],{},[598,941,703],{"mathvariant":701,"lspace":702,"rspace":702},[598,943,706],{},[591,945,946,948],{},[594,947,596],{},[598,949,600],{},[598,951,952],{},"−",[696,954,709],{},[602,956,957],{"encoding":604},"\\alpha' = 180^\\circ - \\alpha",[572,959,961,1008,1056],{"className":960,"ariaHidden":610},[609],[572,962,964,967,999,1002,1005],{"className":963},[614],[572,965],{"className":966,"style":749},[618],[572,968,970,973],{"className":969},[623],[572,971,709],{"className":972,"style":786},[623,735],[572,974,976],{"className":975},[635],[572,977,979],{"className":978},[639],[572,980,982],{"className":981},[643],[572,983,985],{"className":984,"style":749},[647],[572,986,987,990],{"style":650},[572,988],{"className":989,"style":655},[654],[572,991,993],{"className":992},[659,660,661,662],[572,994,996],{"className":995},[623,662],[572,997,703],{"className":998},[623,662],[572,1000],{"className":1001,"style":768},[767],[572,1003,706],{"className":1004},[772],[572,1006],{"className":1007,"style":768},[767],[572,1009,1011,1015,1018,1047,1050,1053],{"className":1010},[614],[572,1012],{"className":1013,"style":1014},[618],"height:0.7574em;vertical-align:-0.0833em;",[572,1016,624],{"className":1017},[623],[572,1019,1021,1024],{"className":1020},[623],[572,1022,631],{"className":1023},[623],[572,1025,1027],{"className":1026},[635],[572,1028,1030],{"className":1029},[639],[572,1031,1033],{"className":1032},[643],[572,1034,1036],{"className":1035,"style":619},[647],[572,1037,1038,1041],{"style":650},[572,1039],{"className":1040,"style":655},[654],[572,1042,1044],{"className":1043},[659,660,661,662],[572,1045,600],{"className":1046},[666,662],[572,1048],{"className":1049,"style":790},[767],[572,1051,952],{"className":1052},[666],[572,1054],{"className":1055,"style":790},[767],[572,1057,1059,1063],{"className":1058},[614],[572,1060],{"className":1061,"style":1062},[618],"height:0.4306em;",[572,1064,709],{"className":1065,"style":786},[623,735],". Nach dem Winkelsummensatz ist ",[572,1068,1070,1100],{"className":1069},[575],[572,1071,1073],{"className":1072},[579],[581,1074,1075],{"xmlns":583},[585,1076,1077,1097],{},[588,1078,1079,1081,1083,1089,1091,1093,1095],{},[696,1080,709],{},[598,1082,706],{},[591,1084,1085,1087],{},[594,1086,596],{},[598,1088,600],{},[598,1090,952],{},[696,1092,698],{},[598,1094,952],{},[696,1096,715],{},[602,1098,1099],{"encoding":604},"\\alpha = 180^\\circ - \\beta - \\gamma",[572,1101,1103,1121,1168,1186],{"className":1102,"ariaHidden":610},[609],[572,1104,1106,1109,1112,1115,1118],{"className":1105},[614],[572,1107],{"className":1108,"style":1062},[618],[572,1110,709],{"className":1111,"style":786},[623,735],[572,1113],{"className":1114,"style":768},[767],[572,1116,706],{"className":1117},[772],[572,1119],{"className":1120,"style":768},[767],[572,1122,1124,1127,1130,1159,1162,1165],{"className":1123},[614],[572,1125],{"className":1126,"style":1014},[618],[572,1128,624],{"className":1129},[623],[572,1131,1133,1136],{"className":1132},[623],[572,1134,631],{"className":1135},[623],[572,1137,1139],{"className":1138},[635],[572,1140,1142],{"className":1141},[639],[572,1143,1145],{"className":1144},[643],[572,1146,1148],{"className":1147,"style":619},[647],[572,1149,1150,1153],{"style":650},[572,1151],{"className":1152,"style":655},[654],[572,1154,1156],{"className":1155},[659,660,661,662],[572,1157,600],{"className":1158},[666,662],[572,1160],{"className":1161,"style":790},[767],[572,1163,952],{"className":1164},[666],[572,1166],{"className":1167,"style":790},[767],[572,1169,1171,1174,1177,1180,1183],{"className":1170},[614],[572,1172],{"className":1173,"style":912},[618],[572,1175,698],{"className":1176,"style":736},[623,735],[572,1178],{"className":1179,"style":790},[767],[572,1181,952],{"className":1182},[666],[572,1184],{"className":1185,"style":790},[767],[572,1187,1189,1192],{"className":1188},[614],[572,1190],{"className":1191,"style":803},[618],[572,1193,715],{"className":1194,"style":807},[623,735],". Eingesetzt:",[572,1197,1200],{"className":1198},[1199],"katex-display",[572,1201,1203,1261],{"className":1202},[575],[572,1204,1206],{"className":1205},[579],[581,1207,1209],{"xmlns":583,"display":1208},"block",[585,1210,1211,1258],{},[588,1212,1213,1219,1221,1227,1229,1233,1239,1241,1243,1245,1247,1250,1252,1254,1256],{},[591,1214,1215,1217],{},[696,1216,709],{},[598,1218,703],{"mathvariant":701,"lspace":702,"rspace":702},[598,1220,706],{},[591,1222,1223,1225],{},[594,1224,596],{},[598,1226,600],{},[598,1228,952],{},[598,1230,1232],{"stretchy":1231},"false","(",[591,1234,1235,1237],{},[594,1236,596],{},[598,1238,600],{},[598,1240,952],{},[696,1242,698],{},[598,1244,952],{},[696,1246,715],{},[598,1248,1249],{"stretchy":1231},")",[598,1251,706],{},[696,1253,698],{},[598,1255,712],{},[696,1257,715],{},[602,1259,1260],{"encoding":604},"\\alpha' = 180^\\circ - (180^\\circ - \\beta - \\gamma) = \\beta + \\gamma",[572,1262,1264,1313,1362,1414,1432,1454,1472],{"className":1263,"ariaHidden":610},[609],[572,1265,1267,1271,1304,1307,1310],{"className":1266},[614],[572,1268],{"className":1269,"style":1270},[618],"height:0.8019em;",[572,1272,1274,1277],{"className":1273},[623],[572,1275,709],{"className":1276,"style":786},[623,735],[572,1278,1280],{"className":1279},[635],[572,1281,1283],{"className":1282},[639],[572,1284,1286],{"className":1285},[643],[572,1287,1289],{"className":1288,"style":1270},[647],[572,1290,1292,1295],{"style":1291},"top:-3.113em;margin-right:0.05em;",[572,1293],{"className":1294,"style":655},[654],[572,1296,1298],{"className":1297},[659,660,661,662],[572,1299,1301],{"className":1300},[623,662],[572,1302,703],{"className":1303},[623,662],[572,1305],{"className":1306,"style":768},[767],[572,1308,706],{"className":1309},[772],[572,1311],{"className":1312,"style":768},[767],[572,1314,1316,1320,1323,1353,1356,1359],{"className":1315},[614],[572,1317],{"className":1318,"style":1319},[618],"height:0.8074em;vertical-align:-0.0833em;",[572,1321,624],{"className":1322},[623],[572,1324,1326,1329],{"className":1325},[623],[572,1327,631],{"className":1328},[623],[572,1330,1332],{"className":1331},[635],[572,1333,1335],{"className":1334},[639],[572,1336,1338],{"className":1337},[643],[572,1339,1342],{"className":1340,"style":1341},[647],"height:0.7241em;",[572,1343,1344,1347],{"style":1291},[572,1345],{"className":1346,"style":655},[654],[572,1348,1350],{"className":1349},[659,660,661,662],[572,1351,600],{"className":1352},[666,662],[572,1354],{"className":1355,"style":790},[767],[572,1357,952],{"className":1358},[666],[572,1360],{"className":1361,"style":790},[767],[572,1363,1365,1369,1373,1376,1405,1408,1411],{"className":1364},[614],[572,1366],{"className":1367,"style":1368},[618],"height:1em;vertical-align:-0.25em;",[572,1370,1232],{"className":1371},[1372],"mopen",[572,1374,624],{"className":1375},[623],[572,1377,1379,1382],{"className":1378},[623],[572,1380,631],{"className":1381},[623],[572,1383,1385],{"className":1384},[635],[572,1386,1388],{"className":1387},[639],[572,1389,1391],{"className":1390},[643],[572,1392,1394],{"className":1393,"style":1341},[647],[572,1395,1396,1399],{"style":1291},[572,1397],{"className":1398,"style":655},[654],[572,1400,1402],{"className":1401},[659,660,661,662],[572,1403,600],{"className":1404},[666,662],[572,1406],{"className":1407,"style":790},[767],[572,1409,952],{"className":1410},[666],[572,1412],{"className":1413,"style":790},[767],[572,1415,1417,1420,1423,1426,1429],{"className":1416},[614],[572,1418],{"className":1419,"style":912},[618],[572,1421,698],{"className":1422,"style":736},[623,735],[572,1424],{"className":1425,"style":790},[767],[572,1427,952],{"className":1428},[666],[572,1430],{"className":1431,"style":790},[767],[572,1433,1435,1438,1441,1445,1448,1451],{"className":1434},[614],[572,1436],{"className":1437,"style":1368},[618],[572,1439,715],{"className":1440,"style":807},[623,735],[572,1442,1249],{"className":1443},[1444],"mclose",[572,1446],{"className":1447,"style":768},[767],[572,1449,706],{"className":1450},[772],[572,1452],{"className":1453,"style":768},[767],[572,1455,1457,1460,1463,1466,1469],{"className":1456},[614],[572,1458],{"className":1459,"style":912},[618],[572,1461,698],{"className":1462,"style":736},[623,735],[572,1464],{"className":1465,"style":790},[767],[572,1467,712],{"className":1468},[666],[572,1470],{"className":1471,"style":790},[767],[572,1473,1475,1478],{"className":1474},[614],[572,1476],{"className":1477,"style":803},[618],[572,1479,715],{"className":1480,"style":807},[623,735],[558,1482,1484],{"id":1483},"beispiele","Beispiele",[563,1486,1487,1488,808,1574,1660,1661,1691],{},"In einem Dreieck sind ",[572,1489,1491,1514],{"className":1490},[575],[572,1492,1494],{"className":1493},[579],[581,1495,1496],{"xmlns":583},[585,1497,1498,1511],{},[588,1499,1500,1502,1504],{},[696,1501,698],{},[598,1503,706],{},[591,1505,1506,1509],{},[594,1507,1508],{},"50",[598,1510,600],{},[602,1512,1513],{"encoding":604},"\\beta = 50^\\circ",[572,1515,1517,1535],{"className":1516,"ariaHidden":610},[609],[572,1518,1520,1523,1526,1529,1532],{"className":1519},[614],[572,1521],{"className":1522,"style":912},[618],[572,1524,698],{"className":1525,"style":736},[623,735],[572,1527],{"className":1528,"style":768},[767],[572,1530,706],{"className":1531},[772],[572,1533],{"className":1534,"style":768},[767],[572,1536,1538,1541,1545],{"className":1537},[614],[572,1539],{"className":1540,"style":619},[618],[572,1542,1544],{"className":1543},[623],"5",[572,1546,1548,1551],{"className":1547},[623],[572,1549,631],{"className":1550},[623],[572,1552,1554],{"className":1553},[635],[572,1555,1557],{"className":1556},[639],[572,1558,1560],{"className":1559},[643],[572,1561,1563],{"className":1562,"style":619},[647],[572,1564,1565,1568],{"style":650},[572,1566],{"className":1567,"style":655},[654],[572,1569,1571],{"className":1570},[659,660,661,662],[572,1572,600],{"className":1573},[666,662],[572,1575,1577,1600],{"className":1576},[575],[572,1578,1580],{"className":1579},[579],[581,1581,1582],{"xmlns":583},[585,1583,1584,1597],{},[588,1585,1586,1588,1590],{},[696,1587,715],{},[598,1589,706],{},[591,1591,1592,1595],{},[594,1593,1594],{},"70",[598,1596,600],{},[602,1598,1599],{"encoding":604},"\\gamma = 70^\\circ",[572,1601,1603,1621],{"className":1602,"ariaHidden":610},[609],[572,1604,1606,1609,1612,1615,1618],{"className":1605},[614],[572,1607],{"className":1608,"style":803},[618],[572,1610,715],{"className":1611,"style":807},[623,735],[572,1613],{"className":1614,"style":768},[767],[572,1616,706],{"className":1617},[772],[572,1619],{"className":1620,"style":768},[767],[572,1622,1624,1627,1631],{"className":1623},[614],[572,1625],{"className":1626,"style":619},[618],[572,1628,1630],{"className":1629},[623],"7",[572,1632,1634,1637],{"className":1633},[623],[572,1635,631],{"className":1636},[623],[572,1638,1640],{"className":1639},[635],[572,1641,1643],{"className":1642},[639],[572,1644,1646],{"className":1645},[643],[572,1647,1649],{"className":1648,"style":619},[647],[572,1650,1651,1654],{"style":650},[572,1652],{"className":1653,"style":655},[654],[572,1655,1657],{"className":1656},[659,660,661,662],[572,1658,600],{"className":1659},[666,662],". Der Außenwinkel bei ",[572,1662,1664,1678],{"className":1663},[575],[572,1665,1667],{"className":1666},[579],[581,1668,1669],{"xmlns":583},[585,1670,1671,1676],{},[588,1672,1673],{},[696,1674,1675],{},"A",[602,1677,1675],{"encoding":604},[572,1679,1681],{"className":1680,"ariaHidden":610},[609],[572,1682,1684,1688],{"className":1683},[614],[572,1685],{"className":1686,"style":1687},[618],"height:0.6833em;",[572,1689,1675],{"className":1690},[623,735]," ist:",[572,1693,1695],{"className":1694},[1199],[572,1696,1698,1741],{"className":1697},[575],[572,1699,1701],{"className":1700},[579],[581,1702,1703],{"xmlns":583,"display":1208},[585,1704,1705,1738],{},[588,1706,1707,1713,1715,1721,1723,1729,1731],{},[591,1708,1709,1711],{},[696,1710,709],{},[598,1712,703],{"mathvariant":701,"lspace":702,"rspace":702},[598,1714,706],{},[591,1716,1717,1719],{},[594,1718,1508],{},[598,1720,600],{},[598,1722,712],{},[591,1724,1725,1727],{},[594,1726,1594],{},[598,1728,600],{},[598,1730,706],{},[591,1732,1733,1736],{},[594,1734,1735],{},"120",[598,1737,600],{},[602,1739,1740],{"encoding":604},"\\alpha' = 50^\\circ + 70^\\circ = 120^\\circ",[572,1742,1744,1791,1838,1885],{"className":1743,"ariaHidden":610},[609],[572,1745,1747,1750,1782,1785,1788],{"className":1746},[614],[572,1748],{"className":1749,"style":1270},[618],[572,1751,1753,1756],{"className":1752},[623],[572,1754,709],{"className":1755,"style":786},[623,735],[572,1757,1759],{"className":1758},[635],[572,1760,1762],{"className":1761},[639],[572,1763,1765],{"className":1764},[643],[572,1766,1768],{"className":1767,"style":1270},[647],[572,1769,1770,1773],{"style":1291},[572,1771],{"className":1772,"style":655},[654],[572,1774,1776],{"className":1775},[659,660,661,662],[572,1777,1779],{"className":1778},[623,662],[572,1780,703],{"className":1781},[623,662],[572,1783],{"className":1784,"style":768},[767],[572,1786,706],{"className":1787},[772],[572,1789],{"className":1790,"style":768},[767],[572,1792,1794,1797,1800,1829,1832,1835],{"className":1793},[614],[572,1795],{"className":1796,"style":1319},[618],[572,1798,1544],{"className":1799},[623],[572,1801,1803,1806],{"className":1802},[623],[572,1804,631],{"className":1805},[623],[572,1807,1809],{"className":1808},[635],[572,1810,1812],{"className":1811},[639],[572,1813,1815],{"className":1814},[643],[572,1816,1818],{"className":1817,"style":1341},[647],[572,1819,1820,1823],{"style":1291},[572,1821],{"className":1822,"style":655},[654],[572,1824,1826],{"className":1825},[659,660,661,662],[572,1827,600],{"className":1828},[666,662],[572,1830],{"className":1831,"style":790},[767],[572,1833,712],{"className":1834},[666],[572,1836],{"className":1837,"style":790},[767],[572,1839,1841,1844,1847,1876,1879,1882],{"className":1840},[614],[572,1842],{"className":1843,"style":1341},[618],[572,1845,1630],{"className":1846},[623],[572,1848,1850,1853],{"className":1849},[623],[572,1851,631],{"className":1852},[623],[572,1854,1856],{"className":1855},[635],[572,1857,1859],{"className":1858},[639],[572,1860,1862],{"className":1861},[643],[572,1863,1865],{"className":1864,"style":1341},[647],[572,1866,1867,1870],{"style":1291},[572,1868],{"className":1869,"style":655},[654],[572,1871,1873],{"className":1872},[659,660,661,662],[572,1874,600],{"className":1875},[666,662],[572,1877],{"className":1878,"style":768},[767],[572,1880,706],{"className":1881},[772],[572,1883],{"className":1884,"style":768},[767],[572,1886,1888,1891,1895],{"className":1887},[614],[572,1889],{"className":1890,"style":1341},[618],[572,1892,1894],{"className":1893},[623],"12",[572,1896,1898,1901],{"className":1897},[623],[572,1899,631],{"className":1900},[623],[572,1902,1904],{"className":1903},[635],[572,1905,1907],{"className":1906},[639],[572,1908,1910],{"className":1909},[643],[572,1911,1913],{"className":1912,"style":1341},[647],[572,1914,1915,1918],{"style":1291},[572,1916],{"className":1917,"style":655},[654],[572,1919,1921],{"className":1920},[659,660,661,662],[572,1922,600],{"className":1923},[666,662],[563,1925,1926,1927,2178,2179,2351],{},"Zur Kontrolle: ",[572,1928,1930,1977],{"className":1929},[575],[572,1931,1933],{"className":1932},[579],[581,1934,1935],{"xmlns":583},[585,1936,1937,1974],{},[588,1938,1939,1941,1943,1949,1951,1957,1959,1965,1967],{},[696,1940,709],{},[598,1942,706],{},[591,1944,1945,1947],{},[594,1946,596],{},[598,1948,600],{},[598,1950,952],{},[591,1952,1953,1955],{},[594,1954,1508],{},[598,1956,600],{},[598,1958,952],{},[591,1960,1961,1963],{},[594,1962,1594],{},[598,1964,600],{},[598,1966,706],{},[591,1968,1969,1972],{},[594,1970,1971],{},"60",[598,1973,600],{},[602,1975,1976],{"encoding":604},"\\alpha = 180^\\circ - 50^\\circ - 70^\\circ = 60^\\circ",[572,1978,1980,1998,2045,2092,2139],{"className":1979,"ariaHidden":610},[609],[572,1981,1983,1986,1989,1992,1995],{"className":1982},[614],[572,1984],{"className":1985,"style":1062},[618],[572,1987,709],{"className":1988,"style":786},[623,735],[572,1990],{"className":1991,"style":768},[767],[572,1993,706],{"className":1994},[772],[572,1996],{"className":1997,"style":768},[767],[572,1999,2001,2004,2007,2036,2039,2042],{"className":2000},[614],[572,2002],{"className":2003,"style":1014},[618],[572,2005,624],{"className":2006},[623],[572,2008,2010,2013],{"className":2009},[623],[572,2011,631],{"className":2012},[623],[572,2014,2016],{"className":2015},[635],[572,2017,2019],{"className":2018},[639],[572,2020,2022],{"className":2021},[643],[572,2023,2025],{"className":2024,"style":619},[647],[572,2026,2027,2030],{"style":650},[572,2028],{"className":2029,"style":655},[654],[572,2031,2033],{"className":2032},[659,660,661,662],[572,2034,600],{"className":2035},[666,662],[572,2037],{"className":2038,"style":790},[767],[572,2040,952],{"className":2041},[666],[572,2043],{"className":2044,"style":790},[767],[572,2046,2048,2051,2054,2083,2086,2089],{"className":2047},[614],[572,2049],{"className":2050,"style":1014},[618],[572,2052,1544],{"className":2053},[623],[572,2055,2057,2060],{"className":2056},[623],[572,2058,631],{"className":2059},[623],[572,2061,2063],{"className":2062},[635],[572,2064,2066],{"className":2065},[639],[572,2067,2069],{"className":2068},[643],[572,2070,2072],{"className":2071,"style":619},[647],[572,2073,2074,2077],{"style":650},[572,2075],{"className":2076,"style":655},[654],[572,2078,2080],{"className":2079},[659,660,661,662],[572,2081,600],{"className":2082},[666,662],[572,2084],{"className":2085,"style":790},[767],[572,2087,952],{"className":2088},[666],[572,2090],{"className":2091,"style":790},[767],[572,2093,2095,2098,2101,2130,2133,2136],{"className":2094},[614],[572,2096],{"className":2097,"style":619},[618],[572,2099,1630],{"className":2100},[623],[572,2102,2104,2107],{"className":2103},[623],[572,2105,631],{"className":2106},[623],[572,2108,2110],{"className":2109},[635],[572,2111,2113],{"className":2112},[639],[572,2114,2116],{"className":2115},[643],[572,2117,2119],{"className":2118,"style":619},[647],[572,2120,2121,2124],{"style":650},[572,2122],{"className":2123,"style":655},[654],[572,2125,2127],{"className":2126},[659,660,661,662],[572,2128,600],{"className":2129},[666,662],[572,2131],{"className":2132,"style":768},[767],[572,2134,706],{"className":2135},[772],[572,2137],{"className":2138,"style":768},[767],[572,2140,2142,2145,2149],{"className":2141},[614],[572,2143],{"className":2144,"style":619},[618],[572,2146,2148],{"className":2147},[623],"6",[572,2150,2152,2155],{"className":2151},[623],[572,2153,631],{"className":2154},[623],[572,2156,2158],{"className":2157},[635],[572,2159,2161],{"className":2160},[639],[572,2162,2164],{"className":2163},[643],[572,2165,2167],{"className":2166,"style":619},[647],[572,2168,2169,2172],{"style":650},[572,2170],{"className":2171,"style":655},[654],[572,2173,2175],{"className":2174},[659,660,661,662],[572,2176,600],{"className":2177},[666,662],", und ",[572,2180,2182,2216],{"className":2181},[575],[572,2183,2185],{"className":2184},[579],[581,2186,2187],{"xmlns":583},[585,2188,2189,2213],{},[588,2190,2191,2197,2199,2205,2207],{},[591,2192,2193,2195],{},[594,2194,596],{},[598,2196,600],{},[598,2198,952],{},[591,2200,2201,2203],{},[594,2202,1971],{},[598,2204,600],{},[598,2206,706],{},[591,2208,2209,2211],{},[594,2210,1735],{},[598,2212,600],{},[602,2214,2215],{"encoding":604},"180^\\circ - 60^\\circ = 120^\\circ",[572,2217,2219,2266,2313],{"className":2218,"ariaHidden":610},[609],[572,2220,2222,2225,2228,2257,2260,2263],{"className":2221},[614],[572,2223],{"className":2224,"style":1014},[618],[572,2226,624],{"className":2227},[623],[572,2229,2231,2234],{"className":2230},[623],[572,2232,631],{"className":2233},[623],[572,2235,2237],{"className":2236},[635],[572,2238,2240],{"className":2239},[639],[572,2241,2243],{"className":2242},[643],[572,2244,2246],{"className":2245,"style":619},[647],[572,2247,2248,2251],{"style":650},[572,2249],{"className":2250,"style":655},[654],[572,2252,2254],{"className":2253},[659,660,661,662],[572,2255,600],{"className":2256},[666,662],[572,2258],{"className":2259,"style":790},[767],[572,2261,952],{"className":2262},[666],[572,2264],{"className":2265,"style":790},[767],[572,2267,2269,2272,2275,2304,2307,2310],{"className":2268},[614],[572,2270],{"className":2271,"style":619},[618],[572,2273,2148],{"className":2274},[623],[572,2276,2278,2281],{"className":2277},[623],[572,2279,631],{"className":2280},[623],[572,2282,2284],{"className":2283},[635],[572,2285,2287],{"className":2286},[639],[572,2288,2290],{"className":2289},[643],[572,2291,2293],{"className":2292,"style":619},[647],[572,2294,2295,2298],{"style":650},[572,2296],{"className":2297,"style":655},[654],[572,2299,2301],{"className":2300},[659,660,661,662],[572,2302,600],{"className":2303},[666,662],[572,2305],{"className":2306,"style":768},[767],[572,2308,706],{"className":2309},[772],[572,2311],{"className":2312,"style":768},[767],[572,2314,2316,2319,2322],{"className":2315},[614],[572,2317],{"className":2318,"style":619},[618],[572,2320,1894],{"className":2321},[623],[572,2323,2325,2328],{"className":2324},[623],[572,2326,631],{"className":2327},[623],[572,2329,2331],{"className":2330},[635],[572,2332,2334],{"className":2333},[639],[572,2335,2337],{"className":2336},[643],[572,2338,2340],{"className":2339,"style":619},[647],[572,2341,2342,2345],{"style":650},[572,2343],{"className":2344,"style":655},[654],[572,2346,2348],{"className":2347},[659,660,661,662],[572,2349,600],{"className":2350},[666,662],".",[563,2353,2354,2355,2419],{},"Ein Außenwinkel ist ",[572,2356,2358,2377],{"className":2357},[575],[572,2359,2361],{"className":2360},[579],[581,2362,2363],{"xmlns":583},[585,2364,2365,2374],{},[588,2366,2367],{},[591,2368,2369,2372],{},[594,2370,2371],{},"135",[598,2373,600],{},[602,2375,2376],{"encoding":604},"135^\\circ",[572,2378,2380],{"className":2379,"ariaHidden":610},[609],[572,2381,2383,2386,2390],{"className":2382},[614],[572,2384],{"className":2385,"style":619},[618],[572,2387,2389],{"className":2388},[623],"13",[572,2391,2393,2396],{"className":2392},[623],[572,2394,1544],{"className":2395},[623],[572,2397,2399],{"className":2398},[635],[572,2400,2402],{"className":2401},[639],[572,2403,2405],{"className":2404},[643],[572,2406,2408],{"className":2407,"style":619},[647],[572,2409,2410,2413],{"style":650},[572,2411],{"className":2412,"style":655},[654],[572,2414,2416],{"className":2415},[659,660,661,662],[572,2417,600],{"className":2418},[666,662]," groß, einer der nicht anliegenden Innenwinkel ist ein rechter Winkel. Der andere ist dann:",[572,2421,2423],{"className":2422},[1199],[572,2424,2426,2462],{"className":2425},[575],[572,2427,2429],{"className":2428},[579],[581,2430,2431],{"xmlns":583,"display":1208},[585,2432,2433,2459],{},[588,2434,2435,2441,2443,2450,2452],{},[591,2436,2437,2439],{},[594,2438,2371],{},[598,2440,600],{},[598,2442,952],{},[591,2444,2445,2448],{},[594,2446,2447],{},"90",[598,2449,600],{},[598,2451,706],{},[591,2453,2454,2457],{},[594,2455,2456],{},"45",[598,2458,600],{},[602,2460,2461],{"encoding":604},"135^\\circ - 90^\\circ = 45^\\circ",[572,2463,2465,2512,2560],{"className":2464,"ariaHidden":610},[609],[572,2466,2468,2471,2474,2503,2506,2509],{"className":2467},[614],[572,2469],{"className":2470,"style":1319},[618],[572,2472,2389],{"className":2473},[623],[572,2475,2477,2480],{"className":2476},[623],[572,2478,1544],{"className":2479},[623],[572,2481,2483],{"className":2482},[635],[572,2484,2486],{"className":2485},[639],[572,2487,2489],{"className":2488},[643],[572,2490,2492],{"className":2491,"style":1341},[647],[572,2493,2494,2497],{"style":1291},[572,2495],{"className":2496,"style":655},[654],[572,2498,2500],{"className":2499},[659,660,661,662],[572,2501,600],{"className":2502},[666,662],[572,2504],{"className":2505,"style":790},[767],[572,2507,952],{"className":2508},[666],[572,2510],{"className":2511,"style":790},[767],[572,2513,2515,2518,2522,2551,2554,2557],{"className":2514},[614],[572,2516],{"className":2517,"style":1341},[618],[572,2519,2521],{"className":2520},[623],"9",[572,2523,2525,2528],{"className":2524},[623],[572,2526,631],{"className":2527},[623],[572,2529,2531],{"className":2530},[635],[572,2532,2534],{"className":2533},[639],[572,2535,2537],{"className":2536},[643],[572,2538,2540],{"className":2539,"style":1341},[647],[572,2541,2542,2545],{"style":1291},[572,2543],{"className":2544,"style":655},[654],[572,2546,2548],{"className":2547},[659,660,661,662],[572,2549,600],{"className":2550},[666,662],[572,2552],{"className":2553,"style":768},[767],[572,2555,706],{"className":2556},[772],[572,2558],{"className":2559,"style":768},[767],[572,2561,2563,2566,2570],{"className":2562},[614],[572,2564],{"className":2565,"style":1341},[618],[572,2567,2569],{"className":2568},[623],"4",[572,2571,2573,2576],{"className":2572},[623],[572,2574,1544],{"className":2575},[623],[572,2577,2579],{"className":2578},[635],[572,2580,2582],{"className":2581},[639],[572,2583,2585],{"className":2584},[643],[572,2586,2588],{"className":2587,"style":1341},[647],[572,2589,2590,2593],{"style":1291},[572,2591],{"className":2592,"style":655},[654],[572,2594,2596],{"className":2595},[659,660,661,662],[572,2597,600],{"className":2598},[666,662],[558,2600,2602],{"id":2601},"typische-fehler","Typische Fehler",[2604,2605,2606,2613,2616],"ul",{},[2607,2608,2609,2610,2612],"li",{},"Den Innenwinkel an derselben Ecke mitzählen. Es zählen nur die beiden Innenwinkel an den ",[567,2611,676],{}," Ecken.",[2607,2614,2615],{},"Außenwinkel und Scheitelwinkel verwechseln. Der Außenwinkel liegt neben dem Innenwinkel auf der Verlängerung einer Seite.",[2607,2617,2618,2619,2680,2681,2351],{},"Annehmen, die drei Außenwinkel ergäben zusammen ",[572,2620,2622,2639],{"className":2621},[575],[572,2623,2625],{"className":2624},[579],[581,2626,2627],{"xmlns":583},[585,2628,2629,2637],{},[588,2630,2631],{},[591,2632,2633,2635],{},[594,2634,596],{},[598,2636,600],{},[602,2638,605],{"encoding":604},[572,2640,2642],{"className":2641,"ariaHidden":610},[609],[572,2643,2645,2648,2651],{"className":2644},[614],[572,2646],{"className":2647,"style":619},[618],[572,2649,624],{"className":2650},[623],[572,2652,2654,2657],{"className":2653},[623],[572,2655,631],{"className":2656},[623],[572,2658,2660],{"className":2659},[635],[572,2661,2663],{"className":2662},[639],[572,2664,2666],{"className":2665},[643],[572,2667,2669],{"className":2668,"style":619},[647],[572,2670,2671,2674],{"style":650},[572,2672],{"className":2673,"style":655},[654],[572,2675,2677],{"className":2676},[659,660,661,662],[572,2678,600],{"className":2679},[666,662],". Die Summe der drei Außenwinkel (je einer pro Ecke) ist immer 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