Question

in circle d with m∠cfe = 30°, find the measure of minor arc \\(\overarc{ce}\\).
answer attempt 1 out of 3
m \\(\overarc{ce}\\)= ° submit answer

Explanation:

Step1: Recall Inscribed Angle Theorem

The measure of an inscribed angle is half the measure of its intercepted arc. Here, $\angle CFE$ is an inscribed angle intercepting arc $CE$.

Step2: Calculate Arc Measure

Let $m\overarc{CE}$ be the measure of arc $CE$. By the Inscribed Angle Theorem, $m\angle CFE=\frac{1}{2}m\overarc{CE}$. Given $m\angle CFE = 30^\circ$, we solve for $m\overarc{CE}$:
$30^\circ=\frac{1}{2}m\overarc{CE}$
Multiply both sides by 2: $m\overarc{CE}=2\times30^\circ = 60^\circ$.

Answer:

$60$