Question

the center of the circle is c, and m∠ead = 21°. find meb⌢. enter the correct value in the box.

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of the intercepted arc. Here, $\angle EAD$ is an inscribed angle and $\overparen{EB}$ is the intercepted arc.
Let $m\angle EAD = \theta$ and $m\overparen{EB}=\alpha$. The formula is $\theta=\frac{1}{2}\alpha$.

Step2: Solve for the measure of the arc

Given $\theta = 21^{\circ}$, we can solve for $\alpha$ from the formula $\theta=\frac{1}{2}\alpha$. Rearranging the formula gives $\alpha = 2\theta$.
Substitute $\theta = 21^{\circ}$ into the formula: $\alpha=2\times21^{\circ}=42^{\circ}$.

Answer:

$42^{\circ}$