229:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000 Pensamiento espacial:@0.721207:0.043660:0.914624:0.043660:0.914624:0.024915:0.721207:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 En todo triángulo :@0.087121:0.142257:0.218370:0.142257:0.218370:0.126545:0.087121:0.126545:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 equilátero:@0.218180:0.142257:0.295826:0.142257:0.295826:0.125588:0.218180:0.125588:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , los ángulos interiores son :@0.295730:0.142257:0.491175:0.142257:0.491175:0.126545:0.295730:0.126545:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 congruentes y su medida es 60º.:@0.169567:0.158899:0.404743:0.158899:0.404743:0.143187:0.169567:0.143187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 En todo triángulo :@0.516691:0.142257:0.647940:0.142257:0.647940:0.126545:0.516691:0.126545:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 isósceles:@0.647750:0.142257:0.714363:0.142257:0.714363:0.125588:0.647750:0.125588:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , los ángulos opuestos a los :@0.714256:0.142257:0.915460:0.142257:0.915460:0.126545:0.714256:0.126545:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lados de igual tamaño son congruentes.:@0.568618:0.158899:0.859561:0.158899:0.859561:0.143187:0.568618:0.143187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Gráfica 5.14 triángulo equilátero:@0.165241:0.185069:0.408986:0.185069:0.408986:0.168399:0.165241:0.168399:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.174876:0.344369:0.184955:0.344369:0.184955:0.329455:0.174876:0.329455:0.000000 B:@0.278582:0.212945:0.287508:0.212945:0.287508:0.198031:0.278582:0.198031:0.000000 60°:@0.271978:0.250591:0.294112:0.250591:0.294112:0.235676:0.271978:0.235676:0.000000:0.000000:0.000000 60°:@0.336421:0.323561:0.358555:0.323561:0.358555:0.308647:0.336421:0.308647:0.000000:0.000000:0.000000 60°:@0.209000:0.323425:0.231134:0.323425:0.231134:0.308510:0.209000:0.308510:0.000000:0.000000:0.000000 C:@0.383258:0.344382:0.392810:0.344382:0.392810:0.329467:0.383258:0.329467:0.000000 AB:@0.233666:0.373705:0.252276:0.373705:0.252276:0.357299:0.233666:0.357299:0.000000:0.000000 ≅:@0.256739:0.372342:0.272072:0.372342:0.272072:0.354688:0.256739:0.354688:0.000000 AC:@0.275589:0.372444:0.295267:0.372444:0.295267:0.356038:0.275589:0.356038:0.000000:0.000000 ≅:@0.300347:0.372342:0.315680:0.372342:0.315680:0.354688:0.300347:0.354688:0.000000 BC:@0.318256:0.373686:0.338224:0.373686:0.338224:0.356255:0.318256:0.356255:0.000000:0.000000 Gráfica 5.15 triángulo isósceles:@0.597664:0.185065:0.830372:0.185065:0.830372:0.168395:0.597664:0.168395:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.657287:0.278152:0.665495:0.278152:0.665495:0.262731:0.657287:0.262731:0.000000 a:@0.763427:0.278152:0.771635:0.278152:0.771635:0.262731:0.763427:0.262731:0.000000 b:@0.709276:0.352589:0.718965:0.352589:0.718965:0.337168:0.709276:0.337168:0.000000 :@0.665162:0.325307:0.675488:0.325307:0.675488:0.310459:0.665162:0.310459:0.000000 :@0.752643:0.325307:0.762969:0.325307:0.762969:0.310459:0.752643:0.310459:0.000000 :@0.709189:0.243570:0.719515:0.243570:0.719515:0.228723:0.709189:0.228723:0.000000 AC:@0.681538:0.376464:0.701215:0.376464:0.701215:0.360057:0.681538:0.360057:0.000000:0.000000 ≅:@0.706297:0.376361:0.721630:0.376361:0.721630:0.358707:0.706297:0.358707:0.000000 BC:@0.724206:0.377705:0.744174:0.377705:0.744174:0.360274:0.724206:0.360274:0.000000:0.000000 Ejemplo 1:@0.073089:0.396373:0.149460:0.396373:0.149460:0.379704:0.073089:0.379704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Halla la medida de los ángulos y mostrados en la figura:@0.073089:0.416588:0.493842:0.416588:0.493842:0.400875:0.073089:0.400875:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.297455:0.416588:0.328232:0.416588:0.328232:0.400182:0.297455:0.400182:0.000000:0.000000:0.000000 Gráfica 5.16 ángulos interiores:@0.117008:0.440649:0.345879:0.440649:0.345879:0.423980:0.117008:0.423980:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 79°:@0.262329:0.525839:0.285595:0.525839:0.285595:0.510201:0.262329:0.510201:0.000000:0.000000:0.000000 46°:@0.214405:0.567950:0.237671:0.567950:0.237671:0.552312:0.214405:0.552312:0.000000:0.000000:0.000000 x:@0.326229:0.567950:0.333648:0.567950:0.333648:0.551622:0.326229:0.551622:0.000000 y:@0.171738:0.561076:0.179176:0.561076:0.179176:0.544748:0.171738:0.544748:0.000000 La suma de los ángulos interiores del triángulo es 180º:@0.396408:0.461239:0.790461:0.461239:0.790461:0.445526:0.396408:0.445526:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Luego, :@0.396408:0.477880:0.449295:0.477880:0.449295:0.462168:0.396408:0.462168:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.449181:0.477880:0.456636:0.477880:0.456636:0.461474:0.449181:0.461474:0.000000 +:@0.456563:0.478463:0.471896:0.478463:0.471896:0.460809:0.456563:0.460809:0.000000 79º 46º 180º:@0.471804:0.477880:0.583076:0.477880:0.583076:0.462168:0.471804:0.462168:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 +:@0.495733:0.478463:0.511067:0.478463:0.511067:0.460809:0.495733:0.460809:0.000000 =:@0.534904:0.478463:0.550237:0.478463:0.550237:0.460809:0.534904:0.460809:0.000000 x:@0.606508:0.494522:0.613963:0.494522:0.613963:0.478116:0.606508:0.478116:0.000000 +:@0.613889:0.495105:0.629223:0.495105:0.629223:0.477450:0.613889:0.477450:0.000000 125º 180º:@0.629131:0.494522:0.710123:0.494522:0.710123:0.478810:0.629131:0.478810:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 =:@0.661951:0.495105:0.677284:0.495105:0.677284:0.477450:0.661951:0.477450:0.000000 x:@0.634984:0.511164:0.642439:0.511164:0.642439:0.494758:0.634984:0.494758:0.000000 =:@0.642365:0.511746:0.657699:0.511746:0.657699:0.494092:0.642365:0.494092:0.000000 55º:@0.657607:0.511164:0.681628:0.511164:0.681628:0.495451:0.657607:0.495451:0.000000:0.000000:0.000000 y:@0.396389:0.527806:0.403863:0.527806:0.403863:0.511400:0.396389:0.511400:0.000000 es ángulo exterior. Por el teorema anterior,:@0.403789:0.527806:0.713197:0.527806:0.713197:0.512093:0.403789:0.512093:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.623645:0.544448:0.631119:0.544448:0.631119:0.528042:0.623645:0.528042:0.000000 =:@0.631045:0.545030:0.646378:0.545030:0.646378:0.527376:0.631045:0.527376:0.000000 79º:@0.646286:0.544448:0.670308:0.544448:0.670308:0.528735:0.646286:0.528735:0.000000:0.000000:0.000000 +:@0.670216:0.545030:0.685549:0.545030:0.685549:0.527376:0.670216:0.527376:0.000000 x:@0.685457:0.544448:0.692912:0.544448:0.692912:0.528042:0.685457:0.528042:0.000000 Reemplazando el valor de , obtenemos:@0.396371:0.561090:0.687106:0.561090:0.687106:0.545377:0.396371:0.545377:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.588248:0.561090:0.595703:0.561090:0.595703:0.544683:0.588248:0.544683:0.000000 y:@0.615362:0.577731:0.622835:0.577731:0.622835:0.561325:0.615362:0.561325:0.000000 =:@0.622762:0.578314:0.638095:0.578314:0.638095:0.560660:0.622762:0.560660:0.000000 79º 55º:@0.638003:0.577731:0.701195:0.577731:0.701195:0.562019:0.638003:0.562019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 +:@0.661932:0.578314:0.677266:0.578314:0.677266:0.560660:0.661932:0.560660:0.000000 y:@0.630493:0.594373:0.637966:0.594373:0.637966:0.577967:0.630493:0.577967:0.000000 =:@0.637893:0.594956:0.653226:0.594956:0.653226:0.577301:0.637893:0.577301:0.000000 134º:@0.653134:0.594373:0.686064:0.594373:0.686064:0.578661:0.653134:0.578661:0.000000:0.000000:0.000000:0.000000 Ejemplo 2:@0.073048:0.635173:0.149419:0.635173:0.149419:0.618504:0.073048:0.618504:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Halla la medida de los ángulos interiores del triángulo mostrado en la figura:@0.073048:0.655393:0.620875:0.655393:0.620875:0.639681:0.073048:0.639681:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Gráfica 5.17 ángulos exteriores:@0.115237:0.681992:0.347583:0.681992:0.347583:0.665323:0.115237:0.665323:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 15°:@0.250671:0.799661:0.299456:0.799661:0.299456:0.784024:0.250671:0.784024:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.259611:0.799661:0.267030:0.799661:0.267030:0.783333:0.259611:0.783333:0.000000 :@0.267030:0.800241:0.276190:0.800241:0.276190:0.782671:0.267030:0.782671:0.000000 139°:@0.158651:0.834374:0.190857:0.834374:0.190857:0.818736:0.158651:0.818736:0.000000:0.000000:0.000000:0.000000 x:@0.304183:0.835975:0.311602:0.835975:0.311602:0.819647:0.304183:0.819647:0.000000 :@0.311602:0.836555:0.320762:0.836555:0.320762:0.818985:0.311602:0.818985:0.000000 8°:@0.320762:0.835975:0.335088:0.835975:0.335088:0.820337:0.320762:0.820337:0.000000:0.000000 y:@0.217805:0.832939:0.225243:0.832939:0.225243:0.816611:0.217805:0.816611:0.000000 139º es un ángulo exterior. Luego, su medida es igual a la suma de las :@0.396408:0.679456:0.924273:0.679456:0.924273:0.663743:0.396408:0.663743:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 medidas de los ángulos interiores no adyascentes::@0.396408:0.696098:0.759572:0.696098:0.759572:0.680385:0.396408:0.680385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 139 2:@0.588745:0.712740:0.644096:0.712740:0.644096:0.697027:0.588745:0.697027:0.000000:0.000000:0.000000:0.000000:0.000000 =:@0.618767:0.713322:0.634101:0.713322:0.634101:0.695668:0.618767:0.695668:0.000000 x:@0.645127:0.712740:0.652581:0.712740:0.652581:0.696333:0.645127:0.696333:0.000000 –:@0.653612:0.713322:0.662816:0.713322:0.662816:0.695668:0.653612:0.695668:0.000000 15:@0.663828:0.712740:0.682825:0.712740:0.682825:0.697027:0.663828:0.697027:0.000000:0.000000 + –:@0.683837:0.713322:0.717872:0.713322:0.717872:0.695668:0.683837:0.695668:0.000000:0.000000:0.000000 x:@0.700183:0.712740:0.707638:0.712740:0.707638:0.696333:0.700183:0.696333:0.000000 8:@0.718884:0.712740:0.727867:0.712740:0.727867:0.697027:0.718884:0.697027:0.000000 139º 3:@0.607649:0.729381:0.670216:0.729381:0.670216:0.713669:0.607649:0.713669:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 =:@0.644887:0.729964:0.660221:0.729964:0.660221:0.712310:0.644887:0.712310:0.000000 x:@0.671246:0.729381:0.678701:0.729381:0.678701:0.712975:0.671246:0.712975:0.000000 –:@0.679732:0.729964:0.688936:0.729964:0.688936:0.712310:0.679732:0.712310:0.000000 23:@0.689948:0.729381:0.708945:0.729381:0.708945:0.713669:0.689948:0.713669:0.000000:0.000000 139º 23º 3:@0.600968:0.746023:0.707122:0.746023:0.707122:0.730311:0.600968:0.730311:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 +:@0.638205:0.746606:0.653539:0.746606:0.653539:0.728951:0.638205:0.728951:0.000000 =:@0.681794:0.746606:0.697127:0.746606:0.697127:0.728951:0.681794:0.728951:0.000000 x:@0.708153:0.746023:0.715608:0.746023:0.715608:0.729617:0.708153:0.729617:0.000000 162º 3:@0.622762:0.762665:0.685328:0.762665:0.685328:0.746952:0.622762:0.746952:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 =:@0.660000:0.763247:0.675333:0.763247:0.675333:0.745593:0.660000:0.745593:0.000000 x:@0.686359:0.762665:0.693814:0.762665:0.693814:0.746259:0.686359:0.746259:0.000000 54º:@0.632775:0.779307:0.659006:0.779307:0.659006:0.763594:0.632775:0.763594:0.000000:0.000000:0.000000 =:@0.660018:0.779889:0.675351:0.779889:0.675351:0.762235:0.660018:0.762235:0.000000 x:@0.676364:0.779307:0.683819:0.779307:0.683819:0.762901:0.676364:0.762901:0.000000 Luego, :@0.396389:0.795949:0.449351:0.795949:0.449351:0.780236:0.396389:0.780236:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.510846:0.812591:0.519828:0.812591:0.519828:0.796878:0.510846:0.796878:0.000000 x:@0.520859:0.812591:0.528314:0.812591:0.528314:0.796184:0.520859:0.796184:0.000000 –:@0.529345:0.813173:0.538549:0.813173:0.538549:0.795519:0.529345:0.795519:0.000000 15º 2 54º 15º 108º 15º 93º:@0.539561:0.812591:0.805767:0.812591:0.805767:0.796878:0.539561:0.796878:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = (:@0.566804:0.813173:0.599292:0.813173:0.599292:0.795519:0.566804:0.795519:0.000000:0.000000:0.000000 )–:@0.627548:0.813173:0.643893:0.813173:0.643893:0.795519:0.627548:0.795519:0.000000:0.000000 =:@0.672148:0.813173:0.687482:0.813173:0.687482:0.795519:0.672148:0.795519:0.000000 –:@0.725732:0.813173:0.734936:0.813173:0.734936:0.795519:0.725732:0.795519:0.000000 =:@0.763191:0.813173:0.778524:0.813173:0.778524:0.795519:0.763191:0.795519:0.000000 x:@0.583536:0.829232:0.590991:0.829232:0.590991:0.812826:0.583536:0.812826:0.000000 – =:@0.592022:0.829815:0.634800:0.829815:0.634800:0.812161:0.592022:0.812161:0.000000:0.000000:0.000000 8º 54º 8º 46º:@0.602238:0.829232:0.733076:0.829232:0.733076:0.813520:0.602238:0.813520:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 – =:@0.663055:0.829815:0.705834:0.829815:0.705834:0.812161:0.663055:0.812161:0.000000:0.000000:0.000000 Para hallar y, recordemos que la suma de las medidas de los ángulos :@0.396389:0.845874:0.924166:0.845874:0.924166:0.830162:0.396389:0.830162:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 interiores de un triángulo es 180º::@0.396389:0.862516:0.639980:0.862516:0.639980:0.846803:0.396389:0.846803:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.584162:0.879158:0.591635:0.879158:0.591635:0.862752:0.584162:0.862752:0.000000 +:@0.592666:0.879740:0.607999:0.879740:0.607999:0.862086:0.592666:0.862086:0.000000 93º 46º 180º:@0.609012:0.879158:0.732432:0.879158:0.732432:0.863445:0.609012:0.863445:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 +:@0.636254:0.879740:0.651588:0.879740:0.651588:0.862086:0.636254:0.862086:0.000000 =:@0.679843:0.879740:0.695176:0.879740:0.695176:0.862086:0.679843:0.862086:0.000000 y:@0.590291:0.895800:0.597765:0.895800:0.597765:0.879394:0.590291:0.879394:0.000000 =:@0.598795:0.896382:0.614129:0.896382:0.614129:0.878728:0.598795:0.878728:0.000000 180º 93º 46º:@0.615141:0.895800:0.726284:0.895800:0.726284:0.880087:0.615141:0.880087:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 –:@0.652379:0.896382:0.661583:0.896382:0.661583:0.878728:0.652379:0.878728:0.000000 –:@0.689838:0.896382:0.699041:0.896382:0.699041:0.878728:0.689838:0.878728:0.000000 y:@0.632738:0.912442:0.640212:0.912442:0.640212:0.896035:0.632738:0.896035:0.000000 =:@0.641243:0.913024:0.656576:0.913024:0.656576:0.895370:0.641243:0.895370:0.000000 41º:@0.657588:0.912442:0.683819:0.912442:0.683819:0.896729:0.657588:0.896729:0.000000:0.000000:0.000000 la medida de los ángulos son 93°, 46° Y 41°:@0.207862:0.936225:0.792837:0.936225:0.792837:0.920513:0.207862:0.920513:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000