Question

what is m\\(\widehat{ad}\\)? circle c is shown, where \\(\angle abd = 47^{circ}). what is the measure of \\(\angle flr\\)? line rt is tangent to circle f at point l, as shown.

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of the intercepted arc. In the first - circle, $\angle ABD$ is an inscribed angle and $\overset{\frown}{AD}$ is the intercepted arc.

Step2: Calculate the measure of $\overset{\frown}{AD}$

Given $\angle ABD = 47^{\circ}$, by the inscribed - angle theorem $m\overset{\frown}{AD}=2\angle ABD$. So $m\overset{\frown}{AD}=2\times47^{\circ}=94^{\circ}$.

Step3: Recall the property of a tangent - radius

In the second - circle, since $RT$ is tangent to circle $F$ at point $L$, then the radius $FL$ is perpendicular to the tangent $RT$. That is, $\angle FLR = 90^{\circ}$.

Answer:

$m\overset{\frown}{AD}=94^{\circ}$, $\angle FLR = 90^{\circ}$