What is the arc measure of ABC in circle P in degrees

Given:

m∠APB = 74°

To find:

The measure of ACB

Solution:

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

⇒ m(ar AB) = m∠APB

⇒ m(ar AB) = 74°

The complete angle of the circle is 360°.

⇒ m(ar ACB) + m(ar AB) = 360°

⇒ m(ar ACB) + 74° = 360°

Subtract 74° from both sides.

⇒ m(ar ACB) = 286°

The measure of arc ACB is 286°.