Question

1. circle c is shown, where ∠abd = 47°. what is m⌢ad?

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of the intercepted arc. In the given circle, $\angle ABD$ is an inscribed angle and $\overset{\frown}{AD}$ is the intercepted arc.
Let $m\overset{\frown}{AD}=x$. According to the inscribed - angle theorem, $\angle ABD=\frac{1}{2}m\overset{\frown}{AD}$.

Step2: Solve for the arc measure

We know that $\angle ABD = 47^{\circ}$, and $\angle ABD=\frac{1}{2}m\overset{\frown}{AD}$. So, $47^{\circ}=\frac{1}{2}x$.
To find $x$, we multiply both sides of the equation by 2: $x = 2\times47^{\circ}=94^{\circ}$.

Answer:

$94^{\circ}$