Question

Which statement regarding the diagram is true?

A) m∠WXY = m∠YXZ
B) m∠WXY < m∠YZX
C) m∠WXY + m∠YXZ = 180°
D) m∠WXY + m∠XYZ = 180°

Answer 1

basically the answer is c

Answer 2

1. Let the m(YXZ)=a, m(XZY)=b, m(XYZ)=c, m(WXY)=d as in the atached figure.

A) d=a,

no, because clearly the triangle is an acute triangle (all angles clearly < 90°).
So a<90, and d, the supplementary of a, is >90. So d>a

B) d<b.

no, d >90, b<90 so d>b

C) d+a=180°

yes, because an interior angle, and that angles exterior angle are supplementary, that is, their sum is 180°

D) d+c=180°. True only if c=a, so if YZX is isosceles. Otherwise, not true.