Question

48 if the ( moverarc{ac} = 100^circ ), find the measure of the central and inscribed angles.
( mangle aoc = )
( mangle abc = )

Explanation:

Step1: Find central angle \( \angle AOC \)

A central angle's measure equals its intercepted arc's measure. Given \( m\overarc{AC} = 100^\circ \), so \( m\angle AOC = 100^\circ \).

Step2: Find inscribed angle \( \angle ABC \)

An inscribed angle is half the measure of its intercepted arc. The arc \( \overarc{AC} \) is intercepted by \( \angle ABC \), so \( m\angle ABC = \frac{1}{2}m\overarc{AC} = \frac{1}{2} \times 100^\circ = 50^\circ \).

Answer:

\( m\angle AOC = \boldsymbol{100^\circ} \), \( m\angle ABC = \boldsymbol{50^\circ} \)