Bunuel wrote:

In the figure above, what is x + y in terms of z?

(A) 180 – z

(B) 180 + z

(C) z – 180

(D) z + 180

(E) z

Attachment:

2017-08-24_1250.png

1. Vertical angle

The unnamed angle inside the triangle and z are congruent vertical angles.

Sum of interior angles of a triangle = 180

x + y + z = 180

x + y = 180 - z

2. Adjacent to exterior angle

z is on the same line as an exterior angle of the triangle, call it w, whose measure equals the sum of non-adjacent interior angles x and y.

x + y =

wz +

w = 180

Substitute:

z + x + y = 180

x + y = 180 - z

Answer A
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