Question

Figure ABCD is a parallelogram.

Parallelogram A B C D is shown. Angle B is (3 n + 20) degrees and angle D is (6 n minus 25) degrees.

What are the measures of angles B and C?

∠B = 15°; ∠C = 165°
∠B = 65°; ∠C = 115°
∠B = 65°; ∠C = 65°
∠B = 15°; ∠C = 15°

Answer 1

In a parallelogram opposite angles are equal, so set 3n + 20 = 6n − 25.
Solve: 3n + 20 = 6n − 25 ⇒ 45 = 3n ⇒ n = 15.
Then ∠B = 3(15) + 20 = 65°. Adjacent angles are supplementary, so ∠C = 180° − 65° = 115°.

Answer: ∠B = 65°; ∠C = 115°.