Question

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

Explanation:

Step1: Recall tangent - radius property

A tangent to a circle is perpendicular to the radius at the point of tangency. So, $\angle PQR = 90^{\circ}$.

Step2: Use angle - sum property of a triangle

In $\triangle PQR$, the sum of the interior angles of a triangle is $180^{\circ}$. Let $\angle R=x$, $\angle P = 53^{\circ}$ and $\angle Q=90^{\circ}$. Then $x + 53^{\circ}+90^{\circ}=180^{\circ}$.

Step3: Solve for $\angle R$

$x=180^{\circ}-(90^{\circ} + 53^{\circ})=180^{\circ}-143^{\circ}=37^{\circ}$.

Answer:

$37^{\circ}$