Question

Figure ABCD is a parallelogram.

Parallelogram A B C D is shown. Angle B is (2 n + 15) degrees and angle D is (3 n minus 5) degrees.

What are the measures of angles B and D?

∠B = 55°; ∠D = 55°
∠B = 55°; ∠D = 125°
∠B = 97°; ∠D = 97°
∠B = 83°; ∠D = 97°

Answer 1

Opposite angles of a parallelogram are equal, so set 2n + 15 = 3n − 5.
Solve: 2n + 15 = 3n − 5 → 20 = n.
Then angle B = 2(20) + 15 = 55°, and angle D = 3(20) − 5 = 55°.

Answer: ∠B = 55°; ∠D = 55°.