A manufacturer designs a circular ornament with lines of glitter as shown. Identify m∠PSR. m=60

m=30

m=90

m=120

m=120

Step-by-step explanation:

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°.