Question

is tangent to circle P at point Q.

Circle P is shown. Line segment P Q is a radius. Line segment Q R is a tangent that intersects the circle at point Q. A line is drawn from point R to point P and goes through a point on the circle. Angle Q P R is 53 degrees.

What is the measure of angle R?

37°
53°
90°
97°

Answer 1

PQ is a radius to the point of tangency Q, so PQ ⟂ QR and ∠PQR = 90°. In triangle PQR the angles sum to 180°, so ∠R = 180° − 90° − 53° = 37°.

Answer: 37°.