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Answer 1

• 87°

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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°