Find the value of x and y in the parallelogram below.
image of parallelogram WYZX with angle W labeled as 3 y degrees, angle X as y degrees, and angle Z as 3 x degrees
A. x = 60 ; y = 60
B. x = 45; y = 45
C. x = 45; y = 135
D. x = 135; y = 45

Question

Find the value of x and y in the parallelogram below.
image of parallelogram WYZX with angle W labeled as 3 y degrees, angle X as y degrees, and angle Z as 3 x degrees
	A.	x = 60 ; y = 60
	B.	x = 45; y = 45
	C.	x = 45; y = 135
	D.	x = 135; y = 45

directrix · Answer

Side WY of the parallelogram is parallel to side XZ of the parallelogram.
Therefore, angles W and X are supplementary because they are same-side interior angles formed by a transversal WX which cuts parallel segments WY and XZ.

3y + y = 180
4y = 180
y = 45

Angle W has measure 3 (45) = 135.
Angle W is equal in measure to Angle Z because opposite angles of a parallelogram are congruent.

Therefore, angle Z = 135 which is x.

D. x = 135; y = 45 --> Answer