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O ângulo em vermelho é um ângulo interno do triângulo, mas os três valores marcados são ângulos externos, cada um formando um par linear com o respectivo ângulo interno . Assim, os ângulos internos do triângulo são , e . Como a soma dos ângulos internos de um triângulo é 180°, temos: + + = 180. Isso dá 540 − 18x = 180, então 18x = 360 e x = 20. Logo, o ângulo pedido vale 180° − 6x = 180° − 120°
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Vamos resolver o problema passo a passo, usando apenas raciocínio geométrico. Primeiro, observe o ângulo dado de 110° sobre a reta. O ângulo interno do triângulo correspondente a ele é o seu suplementar, pois formam um par linear: 110° + ângulo interno = 180° Logo, o ângulo interno vale 70°. O triângulo indicado possui dois lados marcados como iguais, portanto é um triângulo isósceles. Em um triângulo isósceles, os ângulos da base são iguais. Assim, o outro ângulo da base também mede 70°. So
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