Question

pr and qs are diameters of circle t. what is the measure of sr? 50° 80° 100° 120°

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. $\angle QTR=\angle PTS$. Given $\angle PQT = 40^{\circ}$, and since $\triangle PQT$ and $\triangle RST$ are isosceles triangles (radii of the circle $PT = QT$ and $ST=RT$), and $\angle QTR$ and $\angle PTS$ are vertical angles.

Step2: Use the central - angle theorem

The measure of an arc is equal to the measure of its central angle. The central angle corresponding to arc $\widehat{SR}$ is $\angle STR$. We know that $\angle QTR = 40^{\circ}$, and $\angle STR=180^{\circ}- 2\times40^{\circ}=100^{\circ}$. So the measure of arc $\widehat{SR}$ is $100^{\circ}$.

Answer:

$100^{\circ}$