Answer:
120
Step-by-step explanation:
The measure of the arc QR⏜ intercepted by the inscribed ∠QPR is given.
According to the Inscribed Angle Theorem, the measure of the inscribed angle is equal to one-half the measure of the arc.
m∠QPR=12mQR⏜
Substitute 60° for mQR⏜.
m∠QPR=12(60°)
Simplify.
m∠QPR=30°
The figure shows the same circle as in the beginning of the task. Triangle P R S is highlighted in red. Angle S P R measures 30 degrees.
It is given that m∠SRP=30°. Use the Triangle Sum Theorem to find the measure of the unknown ∠PSR.
m∠SRP+m∠SPR+m∠PSR=180°
Substitute the known values.
30°+30°+m∠PSR=180°
Simplify.
60°+m∠PSR=180°
Subtract 60° from both sides.
m∠PSR=120°
Therefore, m∠PSR=120°.
