Question

Figure PQRS is a parallelogram.

Parallelogram P Q R S is shown. Angle Q is (x + 15) degrees and angle R is (6 x minus 10) degrees.

What are the measures of angles P and S?

∠P = 20°; ∠S = 160°
∠P = 40°; ∠S = 140°
∠P = 140°; ∠S = 40°
∠P = 160°; ∠S = 20°

Answer 1

Adjacent angles in a parallelogram are supplementary, so
(x + 15) + (6x − 10) = 180
7x + 5 = 180 → 7x = 175 → x = 25.

Then ∠Q = 25 + 15 = 40° and ∠R = 6(25) − 10 = 140°. Opposite angles are equal, so ∠P = ∠R = 140° and ∠S = ∠Q = 40°.

Answer: ∠P = 140°; ∠S = 40°.