Question

$\overline{qr}$ is tangent to circle p at point q.
what is the measure of angle r?
$37^\circ$
$53^\circ$
$90^\circ$
$97^\circ$

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 of triangle angles is 180°

In $\triangle PQR$, $\angle QPR + \angle PQR + \angle R = 180^\circ$. Substitute known values: $53^\circ + 90^\circ + \angle R = 180^\circ$.

Step3: Solve for $\angle R$

Calculate $\angle R = 180^\circ - 53^\circ - 90^\circ$
$\angle R = 37^\circ$

Answer:

37°