Question

temos x=120 e um palaleograma abcd calcule a medida de a b e c justificando suas respostas

Answer 1

O valor dos ângulos internos de um paralelogramo é = 360°
então se X = 120 + 60= 180
B= 60
C e A= 120

Answer 2

$\^a = \^c\\\^b = \^d$

$\^x \textsf{ e } \^d \textsf{ s\~ao sumplementares}\\\^x + \^d = 180\textdegree\\120\textdegree + \^d = 180\textdegree\\\^d = 180\textdegree - 120\textdegree\\\^d = 60\textdegree = \^b$

A soma de todos os angulos é 360º

$\^a + \^b + \^c + \^d = 360\textdegree\\\^a + 60\textdegree + \^c + 60\textdegree = 360\textdegree\\\^a + \^c=360\textdegree - 60\textdegree - 60\textdegree\\\^a + \^c= 240\textdegree\\\\\textsf{como }\^a \textsf{ e } \^c \textsf{ s\~ao iguais, temos:}\\\^a = 240\textdegree/2 = 120\textdegree\\\^c = 240\textdegree/2 = 120\textdegree$

Portanto:

$\^a = 120\textdegree\\\^b = 60\textdegree\\\^c = 120\textdegree$