Question

find m∠cfe if mcfe = 302°. enter the correct value in the box. show hints

Explanation:

Step1: Recall circle - angle relationship

The measure of an inscribed angle is half the measure of its intercepted arc. The entire circle has a measure of 360°. The arc $\overset{\frown}{CFE}$ is a major arc with measure 302°. The minor arc $\overset{\frown}{CE}=360 - 302=58^{\circ}$.

Step2: Use inscribed - angle formula

The angle $\angle CFE$ is an inscribed angle that intercepts the minor arc $\overset{\frown}{CE}$. By the inscribed - angle theorem, $m\angle CFE=\frac{1}{2}m\overset{\frown}{CE}$.

Step3: Calculate the angle measure

Substitute $m\overset{\frown}{CE} = 58^{\circ}$ into the formula: $m\angle CFE=\frac{1}{2}\times58^{\circ}=29^{\circ}$.

Answer:

29