What is the arc measure of AC on circle P in degrees?

Given:

∠APE and ∠EPD are congruent.

To find:

The measure of arc AC.

Solution:

Complete angle of a circle = 360°

m∠APE + m∠EPD + m∠DPC + m∠CPB + m∠BPA = 360°

m∠APE + m∠APE + 42° + 74° + 136° = 360°

2 m∠APE + 252° = 360°

Subtract 252° from both sides.

2 m∠APE + 252° - 252° = 360° - 252°

2 m∠APE = 108°

Divide by 2 on both sides.

m∠APE = 54°

Given ∠APE and ∠EPD are congruent.

m∠EPD = 54°

m∠APC = 54° + 54° + 42°

             = 150°

The measure of central angle is congruent to the measure of the intercepted arc.

m(ar AC) = m∠APC

m(ar AC) = 150°

The arc measure of AC on circle P is 150°.

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