Question

In the figure given below, AB || CD, ∠APQ = 50°, and ∠PRD = 127°. Find the measure of ∠x and ∠y.

• A. ${50}^{\circ },{67}^{\circ }$
• B. ${77}^{\circ },{50}^{\circ }$
• C. ${50}^{\circ },{77}^{\circ }$
• D. ${77}^{\circ },{57}^{\circ }$

Answer 1

The correct option is C ${50}^{\circ },{77}^{\circ }$

Since AB || CD,
∠APQ = ∠PQR (Alternate interior angles for the transversal PQ)
⇒ x = 50°
∠APR = ∠PRD (Alternate interior angles for the transversal PR)
⇒ y + 50° = 127°
⇒ y = 127° - 50°
⇒ y = 77°