In the given figure, AB is parallel to CD. PQ = QR. Angle BQS = 72 degrees. What is the value (in degrees) of angle PRQ?
Show answer & explanation
Correct answer: A
Explanation
Given:
AB ∥ CD
PQ = QR
∠BQS = 72°
Vertically opposite angles are equal.
Alternate interior angles formed by parallel lines are equal.
Base angles in an isosceles triangle are equal.
∠BQS = 72° ⇒ ∠AQP = 72°
AB ∥ CD ⇒ ∠QPR = ∠AQP = 72°
PQ = QR ⇒ ∠PRQ = ∠QPR = 72°