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°.