Question

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

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. $\angle PQS = 40^{\circ}$, and it intercepts arc $PS$. So, $m\overset{\frown}{PS}=2\times\angle PQS = 80^{\circ}$.

Step2: Use the property of a semi - circle

Since $PR$ is a diameter, the measure of arc $PSR$ is $180^{\circ}$ (a semi - circle has an arc measure of $180^{\circ}$).

Step3: Find the measure of arc $SR$

We know that $m\overset{\frown}{PSR}=m\overset{\frown}{PS}+m\overset{\frown}{SR}$. So, $m\overset{\frown}{SR}=m\overset{\frown}{PSR}-m\overset{\frown}{PS}$. Substituting the values, $m\overset{\frown}{SR}=180^{\circ}-80^{\circ}=100^{\circ}$.

Answer:

$100^{\circ}$