Question

Jacob is cutting a tile in the shape of a parallelogram. Two opposite angles have measures of (6n − 70)° and (2n + 10)°.

What are the two different angle measures of the parallelogram-shaped tile?

20° and 160°
50° and 130°
30° and 150°
70° and 110°

Answer 1

Opposite angles in a parallelogram are equal, so set the expressions equal:
6n − 70 = 2n + 10
4n = 80 → n = 20.

Then one angle is 6(20) − 70 = 50°. Its adjacent angle is supplementary: 180 − 50 = 130°.

Answer: 50° and 130°.