Question

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

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of the intercepted arc.

Step2: Apply the theorem

If $\angle EAD$ is an inscribed angle and $\overset{\frown}{ED}$ is the intercepted arc, then $m\angle EAD=\frac{1}{2}m\overset{\frown}{ED}$.

Step3: Solve for $m\overset{\frown}{ED}$

Given $m\angle EAD = 21^{\circ}$, we can solve for $m\overset{\frown}{ED}$ by multiplying both sides of the equation $m\angle EAD=\frac{1}{2}m\overset{\frown}{ED}$ by 2. So $m\overset{\frown}{ED}=2\times m\angle EAD$.
$m\overset{\frown}{ED}=2\times21^{\circ}=42^{\circ}$

Answer:

$42$