Answer:
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Use the Inscribed Angle theorem, which states that:
- The measure of an inscribed angle is half the measure of the intercepted arc.
Find the angle measure of ∠PNM, considering the intercepted arc is PLM:
- m∠PNM = (mPLM)/2
- m∠PNM = (360° - mPNM)/2
- m∠PNM = (360° - [64° + 122°])/2
- m∠PNM = 174°/2
- m∠PNM = 87°