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So zerfällt ein konvexes Vieleck mit ",[573,771,773,786],{"className":772},[576],[573,774,776],{"className":775},[580],[582,777,778],{"xmlns":584},[586,779,780,784],{},[589,781,782],{},[592,783,594],{},[596,785,594],{"encoding":598},[573,787,789],{"className":788,"ariaHidden":603},[602],[573,790,792,795],{"className":791},[607],[573,793],{"className":794,"style":612},[611],[573,796,594],{"className":797},[616,617]," Ecken in ",[573,800,802,822],{"className":801},[576],[573,803,805],{"className":804},[580],[582,806,807],{"xmlns":584},[586,808,809,819],{},[589,810,811,813,816],{},[592,812,594],{},[637,814,815],{},"−",[641,817,818],{},"2",[596,820,821],{"encoding":598},"n - 2",[573,823,825,845],{"className":824,"ariaHidden":603},[602],[573,826,828,832,835,839,842],{"className":827},[607],[573,829],{"className":830,"style":831},[611],"height:0.6667em;vertical-align:-0.0833em;",[573,833,594],{"className":834},[616,617],[573,836],{"className":837,"style":838},[662],"margin-right:0.2222em;",[573,840,815],{"className":841},[761],[573,843],{"className":844,"style":838},[662],[573,846,848,851],{"className":847},[607],[573,849],{"className":850,"style":677},[611],[573,852,818],{"className":853},[616]," Dreiecke. Jedes Dreieck hat die Winkelsumme ",[573,856,858,875],{"className":857},[576],[573,859,861],{"className":860},[580],[582,862,863],{"xmlns":584},[586,864,865,873],{},[589,866,867],{},[695,868,869,871],{},[641,870,699],{},[637,872,702],{},[596,874,705],{"encoding":598},[573,876,878],{"className":877,"ariaHidden":603},[602],[573,879,881,884,887],{"className":880},[607],[573,882],{"className":883,"style":715},[611],[573,885,719],{"className":886},[616],[573,888,890,893],{"className":889},[616],[573,891,726],{"className":892},[616],[573,894,896],{"className":895},[730],[573,897,899],{"className":898},[734],[573,900,902],{"className":901},[738],[573,903,905],{"className":904,"style":715},[742],[573,906,907,910],{"style":745},[573,908],{"className":909,"style":750},[749],[573,911,913],{"className":912},[754,755,756,757],[573,914,702],{"className":915},[761,757],", also zusammen ",[573,918,920,954],{"className":919},[576],[573,921,923],{"className":922},[580],[582,924,925],{"xmlns":584},[586,926,927,951],{},[589,928,929,933,935,937,939,942,945],{},[637,930,932],{"stretchy":931},"false","(",[592,934,594],{},[637,936,815],{},[641,938,818],{},[637,940,941],{"stretchy":931},")",[637,943,944],{},"⋅",[695,946,947,949],{},[641,948,699],{},[637,950,702],{},[596,952,953],{"encoding":598},"(n - 2) \\cdot 180^\\circ",[573,955,957,980,1002],{"className":956,"ariaHidden":603},[602],[573,958,960,964,968,971,974,977],{"className":959},[607],[573,961],{"className":962,"style":963},[611],"height:1em;vertical-align:-0.25em;",[573,965,932],{"className":966},[967],"mopen",[573,969,594],{"className":970},[616,617],[573,972],{"className":973,"style":838},[662],[573,975,815],{"className":976},[761],[573,978],{"className":979,"style":838},[662],[573,981,983,986,989,993,996,999],{"className":982},[607],[573,984],{"className":985,"style":963},[611],[573,987,818],{"className":988},[616],[573,990,941],{"className":991},[992],"mclose",[573,994],{"className":995,"style":838},[662],[573,997,944],{"className":998},[761],[573,1000],{"className":1001,"style":838},[662],[573,1003,1005,1008,1011],{"className":1004},[607],[573,1006],{"className":1007,"style":715},[611],[573,1009,719],{"className":1010},[616],[573,1012,1014,1017],{"className":1013},[616],[573,1015,726],{"className":1016},[616],[573,1018,1020],{"className":1019},[730],[573,1021,1023],{"className":1022},[734],[573,1024,1026],{"className":1025},[738],[573,1027,1029],{"className":1028,"style":715},[742],[573,1030,1031,1034],{"style":745},[573,1032],{"className":1033,"style":750},[749],[573,1035,1037],{"className":1036},[754,755,756,757],[573,1038,702],{"className":1039},[761,757],".",[564,1042,1043,1044,1047,1048,1109,1110,1160],{},"Hat das Vieleck eine ",[568,1045,1046],{},"einspringende Ecke"," (einen Innenwinkel über ",[573,1049,1051,1068],{"className":1050},[576],[573,1052,1054],{"className":1053},[580],[582,1055,1056],{"xmlns":584},[586,1057,1058,1066],{},[589,1059,1060],{},[695,1061,1062,1064],{},[641,1063,699],{},[637,1065,702],{},[596,1067,705],{"encoding":598},[573,1069,1071],{"className":1070,"ariaHidden":603},[602],[573,1072,1074,1077,1080],{"className":1073},[607],[573,1075],{"className":1076,"style":715},[611],[573,1078,719],{"className":1079},[616],[573,1081,1083,1086],{"className":1082},[616],[573,1084,726],{"className":1085},[616],[573,1087,1089],{"className":1088},[730],[573,1090,1092],{"className":1091},[734],[573,1093,1095],{"className":1094},[738],[573,1096,1098],{"className":1097,"style":715},[742],[573,1099,1100,1103],{"style":745},[573,1101],{"className":1102,"style":750},[749],[573,1104,1106],{"className":1105},[754,755,756,757],[573,1107,702],{"className":1108},[761,757],"), wählt man die Diagonalen etwas geschickter. Auch dann lässt es sich in ",[573,1111,1113,1130],{"className":1112},[576],[573,1114,1116],{"className":1115},[580],[582,1117,1118],{"xmlns":584},[586,1119,1120,1128],{},[589,1121,1122,1124,1126],{},[592,1123,594],{},[637,1125,815],{},[641,1127,818],{},[596,1129,821],{"encoding":598},[573,1131,1133,1151],{"className":1132,"ariaHidden":603},[602],[573,1134,1136,1139,1142,1145,1148],{"className":1135},[607],[573,1137],{"className":1138,"style":831},[611],[573,1140,594],{"className":1141},[616,617],[573,1143],{"className":1144,"style":838},[662],[573,1146,815],{"className":1147},[761],[573,1149],{"className":1150,"style":838},[662],[573,1152,1154,1157],{"className":1153},[607],[573,1155],{"className":1156,"style":677},[611],[573,1158,818],{"className":1159},[616]," Dreiecke zerlegen, und die Formel gilt genauso.",[559,1162,1164],{"id":1163},"beispiele","Beispiele",[564,1166,1167,1168,1220],{},"Viereck, ",[573,1169,1171,1190],{"className":1170},[576],[573,1172,1174],{"className":1173},[580],[582,1175,1176],{"xmlns":584},[586,1177,1178,1187],{},[589,1179,1180,1182,1184],{},[592,1181,594],{},[637,1183,639],{},[641,1185,1186],{},"4",[596,1188,1189],{"encoding":598},"n = 4",[573,1191,1193,1211],{"className":1192,"ariaHidden":603},[602],[573,1194,1196,1199,1202,1205,1208],{"className":1195},[607],[573,1197],{"className":1198,"style":612},[611],[573,1200,594],{"className":1201},[616,617],[573,1203],{"className":1204,"style":663},[662],[573,1206,639],{"className":1207},[667],[573,1209],{"className":1210,"style":663},[662],[573,1212,1214,1217],{"className":1213},[607],[573,1215],{"className":1216,"style":677},[611],[573,1218,1186],{"className":1219},[616],":",[573,1222,1225],{"className":1223},[1224],"katex-display",[573,1226,1228,1273],{"className":1227},[576],[573,1229,1231],{"className":1230},[580],[582,1232,1234],{"xmlns":584,"display":1233},"block",[586,1235,1236,1270],{},[589,1237,1238,1241,1243,1245,1247,1249,1251,1253,1255,1261,1263],{},[592,1239,1240],{},"S",[637,1242,639],{},[637,1244,932],{"stretchy":931},[641,1246,1186],{},[637,1248,815],{},[641,1250,818],{},[637,1252,941],{"stretchy":931},[637,1254,944],{},[695,1256,1257,1259],{},[641,1258,699],{},[637,1260,702],{},[637,1262,639],{},[695,1264,1265,1268],{},[641,1266,1267],{},"360",[637,1269,702],{},[596,1271,1272],{"encoding":598},"S = (4 - 2) \\cdot 180^\\circ = 360^\\circ",[573,1274,1276,1296,1317,1338,1387],{"className":1275,"ariaHidden":603},[602],[573,1277,1279,1283,1287,1290,1293],{"className":1278},[607],[573,1280],{"className":1281,"style":1282},[611],"height:0.6833em;",[573,1284,1240],{"className":1285,"style":1286},[616,617],"margin-right:0.0576em;",[573,1288],{"className":1289,"style":663},[662],[573,1291,639],{"className":1292},[667],[573,1294],{"className":1295,"style":663},[662],[573,1297,1299,1302,1305,1308,1311,1314],{"className":1298},[607],[573,1300],{"className":1301,"style":963},[611],[573,1303,932],{"className":1304},[967],[573,1306,1186],{"className":1307},[616],[573,1309],{"className":1310,"style":838},[662],[573,1312,815],{"className":1313},[761],[573,1315],{"className":1316,"style":838},[662],[573,1318,1320,1323,1326,1329,1332,1335],{"className":1319},[607],[573,1321],{"className":1322,"style":963},[611],[573,1324,818],{"className":1325},[616],[573,1327,941],{"className":1328},[992],[573,1330],{"className":1331,"style":838},[662],[573,1333,944],{"className":1334},[761],[573,1336],{"className":1337,"style":838},[662],[573,1339,1341,1345,1348,1378,1381,1384],{"className":1340},[607],[573,1342],{"className":1343,"style":1344},[611],"height:0.7241em;",[573,1346,719],{"className":1347},[616],[573,1349,1351,1354],{"className":1350},[616],[573,1352,726],{"className":1353},[616],[573,1355,1357],{"className":1356},[730],[573,1358,1360],{"className":1359},[734],[573,1361,1363],{"className":1362},[738],[573,1364,1366],{"className":1365,"style":1344},[742],[573,1367,1369,1372],{"style":1368},"top:-3.113em;margin-right:0.05em;",[573,1370],{"className":1371,"style":750},[749],[573,1373,1375],{"className":1374},[754,755,756,757],[573,1376,702],{"className":1377},[761,757],[573,1379],{"className":1380,"style":663},[662],[573,1382,639],{"className":1383},[667],[573,1385],{"className":1386,"style":663},[662],[573,1388,1390,1393,1397],{"className":1389},[607],[573,1391],{"className":1392,"style":1344},[611],[573,1394,1396],{"className":1395},[616],"36",[573,1398,1400,1403],{"className":1399},[616],[573,1401,726],{"className":1402},[616],[573,1404,1406],{"className":1405},[730],[573,1407,1409],{"className":1408},[734],[573,1410,1412],{"className":1411},[738],[573,1413,1415],{"className":1414,"style":1344},[742],[573,1416,1417,1420],{"style":1368},[573,1418],{"className":1419,"style":750},[749],[573,1421,1423],{"className":1422},[754,755,756,757],[573,1424,702],{"className":1425},[761,757],[564,1427,1428,1429,1220],{},"Fünfeck, ",[573,1430,1432,1451],{"className":1431},[576],[573,1433,1435],{"className":1434},[580],[582,1436,1437],{"xmlns":584},[586,1438,1439,1448],{},[589,1440,1441,1443,1445],{},[592,1442,594],{},[637,1444,639],{},[641,1446,1447],{},"5",[596,1449,1450],{"encoding":598},"n = 5",[573,1452,1454,1472],{"className":1453,"ariaHidden":603},[602],[573,1455,1457,1460,1463,1466,1469],{"className":1456},[607],[573,1458],{"className":1459,"style":612},[611],[573,1461,594],{"className":1462},[616,617],[573,1464],{"className":1465,"style":663},[662],[573,1467,639],{"className":1468},[667],[573,1470],{"className":1471,"style":663},[662],[573,1473,1475,1478],{"className":1474},[607],[573,1476],{"className":1477,"style":677},[611],[573,1479,1447],{"className":1480},[616],[573,1482,1484],{"className":1483},[1224],[573,1485,1487,1530],{"className":1486},[576],[573,1488,1490],{"className":1489},[580],[582,1491,1492],{"xmlns":584,"display":1233},[586,1493,1494,1527],{},[589,1495,1496,1498,1500,1502,1504,1506,1508,1510,1512,1518,1520],{},[592,1497,1240],{},[637,1499,639],{},[637,1501,932],{"stretchy":931},[641,1503,1447],{},[637,1505,815],{},[641,1507,818],{},[637,1509,941],{"stretchy":931},[637,1511,944],{},[695,1513,1514,1516],{},[641,1515,699],{},[637,1517,702],{},[637,1519,639],{},[695,1521,1522,1525],{},[641,1523,1524],{},"540",[637,1526,702],{},[596,1528,1529],{"encoding":598},"S = (5 - 2) \\cdot 180^\\circ = 540^\\circ",[573,1531,1533,1551,1572,1593,1640],{"className":1532,"ariaHidden":603},[602],[573,1534,1536,1539,1542,1545,1548],{"className":1535},[607],[573,1537],{"className":1538,"style":1282},[611],[573,1540,1240],{"className":1541,"style":1286},[616,617],[573,1543],{"className":1544,"style":663},[662],[573,1546,639],{"className":1547},[667],[573,1549],{"className":1550,"style":663},[662],[573,1552,1554,1557,1560,1563,1566,1569],{"className":1553},[607],[573,1555],{"className":1556,"style":963},[611],[573,1558,932],{"className":1559},[967],[573,1561,1447],{"className":1562},[616],[573,1564],{"className":1565,"style":838},[662],[573,1567,815],{"className":1568},[761],[573,1570],{"className":1571,"style":838},[662],[573,1573,1575,1578,1581,1584,1587,1590],{"className":1574},[607],[573,1576],{"className":1577,"style":963},[611],[573,1579,818],{"className":1580},[616],[573,1582,941],{"className":1583},[992],[573,1585],{"className":1586,"style":838},[662],[573,1588,944],{"className":1589},[761],[573,1591],{"className":1592,"style":838},[662],[573,1594,1596,1599,1602,1631,1634,1637],{"className":1595},[607],[573,1597],{"className":1598,"style":1344},[611],[573,1600,719],{"className":1601},[616],[573,1603,1605,1608],{"className":1604},[616],[573,1606,726],{"className":1607},[616],[573,1609,1611],{"className":1610},[730],[573,1612,1614],{"className":1613},[734],[573,1615,1617],{"className":1616},[738],[573,1618,1620],{"className":1619,"style":1344},[742],[573,1621,1622,1625],{"style":1368},[573,1623],{"className":1624,"style":750},[749],[573,1626,1628],{"className":1627},[754,755,756,757],[573,1629,702],{"className":1630},[761,757],[573,1632],{"className":1633,"style":663},[662],[573,1635,639],{"className":1636},[667],[573,1638],{"className":1639,"style":663},[662],[573,1641,1643,1646,1650],{"className":1642},[607],[573,1644],{"className":1645,"style":1344},[611],[573,1647,1649],{"className":1648},[616],"54",[573,1651,1653,1656],{"className":1652},[616],[573,1654,726],{"className":1655},[616],[573,1657,1659],{"className":1658},[730],[573,1660,1662],{"className":1661},[734],[573,1663,1665],{"className":1664},[738],[573,1666,1668],{"className":1667,"style":1344},[742],[573,1669,1670,1673],{"style":1368},[573,1671],{"className":1672,"style":750},[749],[573,1674,1676],{"className":1675},[754,755,756,757],[573,1677,702],{"className":1678},[761,757],[564,1680,1681,1682,1220],{},"Sechseck, ",[573,1683,1685,1704],{"className":1684},[576],[573,1686,1688],{"className":1687},[580],[582,1689,1690],{"xmlns":584},[586,1691,1692,1701],{},[589,1693,1694,1696,1698],{},[592,1695,594],{},[637,1697,639],{},[641,1699,1700],{},"6",[596,1702,1703],{"encoding":598},"n = 6",[573,1705,1707,1725],{"className":1706,"ariaHidden":603},[602],[573,1708,1710,1713,1716,1719,1722],{"className":1709},[607],[573,1711],{"className":1712,"style":612},[611],[573,1714,594],{"className":1715},[616,617],[573,1717],{"className":1718,"style":663},[662],[573,1720,639],{"className":1721},[667],[573,1723],{"className":1724,"style":663},[662],[573,1726,1728,1731],{"className":1727},[607],[573,1729],{"className":1730,"style":677},[611],[573,1732,1700],{"className":1733},[616],[573,1735,1737],{"className":1736},[1224],[573,1738,1740,1783],{"className":1739},[576],[573,1741,1743],{"className":1742},[580],[582,1744,1745],{"xmlns":584,"display":1233},[586,1746,1747,1780],{},[589,1748,1749,1751,1753,1755,1757,1759,1761,1763,1765,1771,1773],{},[592,1750,1240],{},[637,1752,639],{},[637,1754,932],{"stretchy":931},[641,1756,1700],{},[637,1758,815],{},[641,1760,818],{},[637,1762,941],{"stretchy":931},[637,1764,944],{},[695,1766,1767,1769],{},[641,1768,699],{},[637,1770,702],{},[637,1772,639],{},[695,1774,1775,1778],{},[641,1776,1777],{},"720",[637,1779,702],{},[596,1781,1782],{"encoding":598},"S = (6 - 2) \\cdot 180^\\circ = 720^\\circ",[573,1784,1786,1804,1825,1846,1893],{"className":1785,"ariaHidden":603},[602],[573,1787,1789,1792,1795,1798,1801],{"className":1788},[607],[573,1790],{"className":1791,"style":1282},[611],[573,1793,1240],{"className":1794,"style":1286},[616,617],[573,1796],{"className":1797,"style":663},[662],[573,1799,639],{"className":1800},[667],[573,1802],{"className":1803,"style":663},[662],[573,1805,1807,1810,1813,1816,1819,1822],{"className":1806},[607],[573,1808],{"className":1809,"style":963},[611],[573,1811,932],{"className":1812},[967],[573,1814,1700],{"className":1815},[616],[573,1817],{"className":1818,"style":838},[662],[573,1820,815],{"className":1821},[761],[573,1823],{"className":1824,"style":838},[662],[573,1826,1828,1831,1834,1837,1840,1843],{"className":1827},[607],[573,1829],{"className":1830,"style":963},[611],[573,1832,818],{"className":1833},[616],[573,1835,941],{"className":1836},[992],[573,1838],{"className":1839,"style":838},[662],[573,1841,944],{"className":1842},[761],[573,1844],{"className":1845,"style":838},[662],[573,1847,1849,1852,1855,1884,1887,1890],{"className":1848},[607],[573,1850],{"className":1851,"style":1344},[611],[573,1853,719],{"className":1854},[616],[573,1856,1858,1861],{"className":1857},[616],[573,1859,726],{"className":1860},[616],[573,1862,1864],{"className":1863},[730],[573,1865,1867],{"className":1866},[734],[573,1868,1870],{"className":1869},[738],[573,1871,1873],{"className":1872,"style":1344},[742],[573,1874,1875,1878],{"style":1368},[573,1876],{"className":1877,"style":750},[749],[573,1879,1881],{"className":1880},[754,755,756,757],[573,1882,702],{"className":1883},[761,757],[573,1885],{"className":1886,"style":663},[662],[573,1888,639],{"className":1889},[667],[573,1891],{"className":1892,"style":663},[662],[573,1894,1896,1899,1903],{"className":1895},[607],[573,1897],{"className":1898,"style":1344},[611],[573,1900,1902],{"className":1901},[616],"72",[573,1904,1906,1909],{"className":1905},[616],[573,1907,726],{"className":1908},[616],[573,1910,1912],{"className":1911},[730],[573,1913,1915],{"className":1914},[734],[573,1916,1918],{"className":1917},[738],[573,1919,1921],{"className":1920,"style":1344},[742],[573,1922,1923,1926],{"style":1368},[573,1924],{"className":1925,"style":750},[749],[573,1927,1929],{"className":1928},[754,755,756,757],[573,1930,702],{"className":1931},[761,757],[564,1933,1934,1935,1938,1939,1040],{},"Bei einem ",[568,1936,1937],{},"regelmäßigen"," Sechseck sind alle sechs Winkel gleich groß. Jeder Winkel ist dann ",[573,1940,1942,1973],{"className":1941},[576],[573,1943,1945],{"className":1944},[580],[582,1946,1947],{"xmlns":584},[586,1948,1949,1970],{},[589,1950,1951,1957,1959,1961,1963],{},[695,1952,1953,1955],{},[641,1954,1777],{},[637,1956,702],{},[637,1958,1220],{},[641,1960,1700],{},[637,1962,639],{},[695,1964,1965,1968],{},[641,1966,1967],{},"120",[637,1969,702],{},[596,1971,1972],{"encoding":598},"720^\\circ : 6 = 120^\\circ",[573,1974,1976,2023,2041],{"className":1975,"ariaHidden":603},[602],[573,1977,1979,1982,1985,2014,2017,2020],{"className":1978},[607],[573,1980],{"className":1981,"style":715},[611],[573,1983,1902],{"className":1984},[616],[573,1986,1988,1991],{"className":1987},[616],[573,1989,726],{"className":1990},[616],[573,1992,1994],{"className":1993},[730],[573,1995,1997],{"className":1996},[734],[573,1998,2000],{"className":1999},[738],[573,2001,2003],{"className":2002,"style":715},[742],[573,2004,2005,2008],{"style":745},[573,2006],{"className":2007,"style":750},[749],[573,2009,2011],{"className":2010},[754,755,756,757],[573,2012,702],{"className":2013},[761,757],[573,2015],{"className":2016,"style":663},[662],[573,2018,1220],{"className":2019},[667],[573,2021],{"className":2022,"style":663},[662],[573,2024,2026,2029,2032,2035,2038],{"className":2025},[607],[573,2027],{"className":2028,"style":677},[611],[573,2030,1700],{"className":2031},[616],[573,2033],{"className":2034,"style":663},[662],[573,2036,639],{"className":2037},[667],[573,2039],{"className":2040,"style":663},[662],[573,2042,2044,2047,2051],{"className":2043},[607],[573,2045],{"className":2046,"style":715},[611],[573,2048,2050],{"className":2049},[616],"12",[573,2052,2054,2057],{"className":2053},[616],[573,2055,726],{"className":2056},[616],[573,2058,2060],{"className":2059},[730],[573,2061,2063],{"className":2062},[734],[573,2064,2066],{"className":2065},[738],[573,2067,2069],{"className":2068,"style":715},[742],[573,2070,2071,2074],{"style":745},[573,2072],{"className":2073,"style":750},[749],[573,2075,2077],{"className":2076},[754,755,756,757],[573,2078,702],{"className":2079},[761,757],[559,2081,2083],{"id":2082},"typische-fehler","Typische Fehler",[2085,2086,2087,2255],"ul",{},[2088,2089,2090,2175,2176,2226,2227,1040],"li",{},[573,2091,2093,2115],{"className":2092},[576],[573,2094,2096],{"className":2095},[580],[582,2097,2098],{"xmlns":584},[586,2099,2100,2112],{},[589,2101,2102,2104,2106],{},[592,2103,594],{},[637,2105,944],{},[695,2107,2108,2110],{},[641,2109,699],{},[637,2111,702],{},[596,2113,2114],{"encoding":598},"n \\cdot 180^\\circ",[573,2116,2118,2137],{"className":2117,"ariaHidden":603},[602],[573,2119,2121,2125,2128,2131,2134],{"className":2120},[607],[573,2122],{"className":2123,"style":2124},[611],"height:0.4445em;",[573,2126,594],{"className":2127},[616,617],[573,2129],{"className":2130,"style":838},[662],[573,2132,944],{"className":2133},[761],[573,2135],{"className":2136,"style":838},[662],[573,2138,2140,2143,2146],{"className":2139},[607],[573,2141],{"className":2142,"style":715},[611],[573,2144,719],{"className":2145},[616],[573,2147,2149,2152],{"className":2148},[616],[573,2150,726],{"className":2151},[616],[573,2153,2155],{"className":2154},[730],[573,2156,2158],{"className":2157},[734],[573,2159,2161],{"className":2160},[738],[573,2162,2164],{"className":2163,"style":715},[742],[573,2165,2166,2169],{"style":745},[573,2167],{"className":2168,"style":750},[749],[573,2170,2172],{"className":2171},[754,755,756,757],[573,2173,702],{"className":2174},[761,757]," rechnen. Es sind nur ",[573,2177,2179,2196],{"className":2178},[576],[573,2180,2182],{"className":2181},[580],[582,2183,2184],{"xmlns":584},[586,2185,2186,2194],{},[589,2187,2188,2190,2192],{},[592,2189,594],{},[637,2191,815],{},[641,2193,818],{},[596,2195,821],{"encoding":598},[573,2197,2199,2217],{"className":2198,"ariaHidden":603},[602],[573,2200,2202,2205,2208,2211,2214],{"className":2201},[607],[573,2203],{"className":2204,"style":831},[611],[573,2206,594],{"className":2207},[616,617],[573,2209],{"className":2210,"style":838},[662],[573,2212,815],{"className":2213},[761],[573,2215],{"className":2216,"style":838},[662],[573,2218,2220,2223],{"className":2219},[607],[573,2221],{"className":2222,"style":677},[611],[573,2224,818],{"className":2225},[616]," Dreiecke, nicht ",[573,2228,2230,2243],{"className":2229},[576],[573,2231,2233],{"className":2232},[580],[582,2234,2235],{"xmlns":584},[586,2236,2237,2241],{},[589,2238,2239],{},[592,2240,594],{},[596,2242,594],{"encoding":598},[573,2244,2246],{"className":2245,"ariaHidden":603},[602],[573,2247,2249,2252],{"className":2248},[607],[573,2250],{"className":2251,"style":612},[611],[573,2253,594],{"className":2254},[616,617],[2088,2256,2257,2258,2286],{},"Die Winkelsumme durch ",[573,2259,2261,2274],{"className":2260},[576],[573,2262,2264],{"className":2263},[580],[582,2265,2266],{"xmlns":584},[586,2267,2268,2272],{},[589,2269,2270],{},[592,2271,594],{},[596,2273,594],{"encoding":598},[573,2275,2277],{"className":2276,"ariaHidden":603},[602],[573,2278,2280,2283],{"className":2279},[607],[573,2281],{"className":2282,"style":612},[611],[573,2284,594],{"className":2285},[616,617]," teilen, obwohl das Vieleck nicht regelmäßig ist. Gleich große Winkel gibt es nur beim regelmäßigen Vieleck.",{"title":2288,"searchDepth":2289,"depth":2289,"links":2290},"",2,[2291,2292,2293,2294],{"id":561,"depth":2289,"text":562},{"id":765,"depth":2289,"text":766},{"id":1163,"depth":2289,"text":1164},{"id":2082,"depth":2289,"text":2083},[2296,2300,2302,2304,2306],{"lhs":2297,"rhs":699,"where":2298},"(n - 2) * 180",{"n":2299},3,{"lhs":2301,"rhs":1267},"(4 - 2) * 180",{"lhs":2303,"rhs":1524},"(5 - 2) * 180",{"lhs":2305,"rhs":1777},"(6 - 2) * 180",{"lhs":2307,"rhs":1967},"720 \u002F 6","n \\geq 3","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>≥\u003C\u002Fmo>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\geq 3\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7719em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">3\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md",{"caption":2313,"x":2314,"y":2317,"items":2320},"Fünfeck (n = 5), von einer Ecke aus durch Diagonalen in n − 2 = 3 Dreiecke zerlegt",[2315,2316],-0.9,5.1,[2318,2319],-0.5,4.1,[2321,2336,2341,2344,2349,2353,2357,2361],{"type":2322,"points":2323,"fill":2335},"polygon",[2324,2326,2328,2331,2333],[2325,2325],0,[2327,2325],4,[2329,2330],4.6,2.2,[2330,2332],3.6,[2334,2330],-0.4,true,{"type":2337,"from":2338,"to":2339,"style":2340},"segment",[2325,2325],[2329,2330],"dashed",{"type":2337,"from":2342,"to":2343,"style":2340},[2325,2325],[2330,2332],{"type":2345,"at":2346,"from":2347,"to":2348},"angle",[2325,2325],[2327,2325],[2334,2330],{"type":2345,"at":2350,"from":2351,"to":2352},[2327,2325],[2325,2325],[2329,2330],{"type":2345,"at":2354,"from":2355,"to":2356},[2329,2330],[2327,2325],[2330,2332],{"type":2345,"at":2358,"from":2359,"to":2360},[2330,2332],[2329,2330],[2334,2330],{"type":2345,"at":2362,"from":2363,"to":2364},[2334,2330],[2330,2332],[2325,2325],"\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 288 220.8\" width=\"288\" height=\"220.8\" role=\"img\" aria-label=\"Fünfeck (n = 5), von einer Ecke aus durch Diagonalen in n − 2 = 3 Dreiecke zerlegt\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-polygon-angle-sum-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-polygon-angle-sum-clip\">\u003Crect x=\"0\" y=\"0\" width=\"288\" height=\"220.8\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cpolygon points=\"43.2,196.8 235.2,196.8 264,91.2 148.8,24 24,91.2\" class=\"fig-main fig-fill\"\u002F>\u003Cline x1=\"43.2\" y1=\"196.8\" x2=\"264\" y2=\"91.2\" class=\"fig-dashed\"\u002F>\u003Cline x1=\"43.2\" y1=\"196.8\" x2=\"148.8\" y2=\"24\" class=\"fig-dashed\"\u002F>\u003Cpath d=\"M 43.2 196.8 L 65.2 196.8 A 22 22 0 0 0 39.26 175.15 Z\" class=\"fig-angle\"\u002F>\u003Cpath d=\"M 235.2 196.8 L 240.99 175.58 A 22 22 0 0 0 213.2 196.8 Z\" class=\"fig-angle\"\u002F>\u003Cpath d=\"M 264 91.2 L 245 80.11 A 22 22 0 0 0 258.21 112.42 Z\" class=\"fig-angle\"\u002F>\u003Cpath d=\"M 148.8 24 L 129.43 34.43 A 22 22 0 0 0 167.8 35.09 Z\" class=\"fig-angle\"\u002F>\u003Cpath d=\"M 24 91.2 L 27.94 112.85 A 22 22 0 0 0 43.37 80.77 Z\" class=\"fig-angle\"\u002F>\u003C\u002Fsvg>","polygon-angle-sum","S = (n - 2) \\cdot 180^\\circ","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>S\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsup>\u003Cmn>180\u003C\u002Fmn>\u003Cmo>∘\u003C\u002Fmo>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">S = (n - 2) \\cdot 180^\\circ\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7241em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">18\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7241em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mbin mtight\">∘\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","lower",{},"\u002Fde\u002Fformulas\u002Fmath\u002Fgeometry\u002Finnenwinkelsumme-vieleck",[],[2374],"triangle-angle-sum",{"title":548,"description":2288},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Finnenwinkelsumme-vieleck","Die Innenwinkel eines Vielecks mit n Ecken ergeben zusammen (n − 2) · 180°.",[2379,2380,2381,2382,2322],"winkel","vieleck","winkelsumme","innenwinkel",[2384,2387],{"symbol":1240,"meaning":2385,"symbolHtml":2386},"Summe aller Innenwinkel","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>S\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">S\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":594,"meaning":2388,"symbolHtml":2389},"Anzahl der Ecken","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","yWp-ooSoPLYfcNUw525R3EWwCERQPu74cpNzKncyaw0",[2392],{"stem":2393,"title":2394,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Fwinkelsumme-dreieck","Winkelsumme im Dreieck",1793824269131]