Question

qr is tangent to circle p at point q. what is the measure of angle r? 37° 53° 90° 97°

Explanation:

Step1: Identify right angle at Q

A tangent to a circle forms a 90° angle with the radius at the point of tangency, so $\angle PQR = 90^\circ$.

Step2: Sum angles in triangle PQR

The sum of interior angles in a triangle is $180^\circ$. Let $\angle R = x$.
$\angle QPR + \angle PQR + \angle R = 180^\circ$
Substitute known values: $53^\circ + 90^\circ + x = 180^\circ$

Step3: Solve for $\angle R$

Calculate $x = 180^\circ - 53^\circ - 90^\circ$
$x = 37^\circ$

Answer:

37°