Question

applying theorems
$overline{pr}$ and $overline{qs}$ are diameters of circle t. what is the measure of $overparen{sr}$?
$\bigcirc$ $50^{circ}$
$\bigcirc$ $80^{circ}$
$\bigcirc$ $100^{circ}$
$\bigcirc$ $120^{circ}$

Explanation:

Step1: Identify vertical angles

$\angle PTQ = \angle STR = 40^\circ$

Step2: Relate central angle to arc

The measure of arc $\overparen{SR}$ equals the measure of its central angle $\angle STR$.

Answer:

50° is incorrect, the correct answer corresponding to the calculation is 40°, but since 40° is not listed, recheck: $\triangle PTQ$ and $\triangle STR$ are congruent, $\angle PQT=40^\circ$, $PT=QT$ so $\angle QPT=40^\circ$, $\angle PTQ=180-40-40=100^\circ$, so $\angle STR=100^\circ$, which is the measure of $\overparen{SR}$.

Step1: Calculate central angle $\angle PTQ$

$\angle PTQ = 180^\circ - 40^\circ - 40^\circ = 100^\circ$

Step2: Match vertical angle to arc

$\angle STR = \angle PTQ = 100^\circ$, so $m\overparen{SR}=100^\circ$