Question

Find the value of x, y, and z in the parallelogram 91° on the right x (4y+5)° on the top y (3x-8)° on the left z (-8z-7)° on the bottom

Answer 1

I assume the four angle measures (in order) are:
- right = 91°
- top = (4y + 5)°
- left = (3x − 8)°
- bottom = (−8z − 7)°

In a parallelogram opposite angles are equal and adjacent angles are supplementary. So:

1) left = right:
3x − 8 = 91
3x = 99
x = 33

2) top + right = 180 (supplementary):
(4y + 5) + 91 = 180
4y + 96 = 180
4y = 84
y = 21

3) top = bottom (opposite angles equal):
4y + 5 = −8z − 7
Substitute y = 21:
84 + 5 = −8z − 7
89 = −8z − 7
−8z = 96
z = −12

Check: bottom = −8(−12) − 7 = 96 − 7 = 89, and left = 3(33) − 8 = 91; 89 + 91 = 180, so it is consistent.

Answer: x = 33, y = 21, z = −12. If your diagram labels are different, tell me how the expressions are placed and I’ll rework it.