Question

circle c is shown, where ∠abd = 47°. what is m\\(widehat{ad}\\)?

Explanation:

Step1: Recall inscribed - angle theorem

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

Step2: Identify the inscribed angle and intercepted arc

The inscribed angle is $\angle ABD = 47^{\circ}$, and the intercepted arc is $\overset{\frown}{AD}$.

Step3: Calculate the measure of the arc

Let $m\overset{\frown}{AD}=x$. According to the inscribed - angle theorem, $\angle ABD=\frac{1}{2}m\overset{\frown}{AD}$. So, $x = 2\times\angle ABD$.
Substitute $\angle ABD = 47^{\circ}$ into the formula: $x=2\times47^{\circ}=94^{\circ}$.

Answer:

$94^{\circ}$