Question

the measure of $widehat{de}$ is 132°. what is the measure of $angle def$, the tangent - chord angle?
a. 264°
b. 132°
c. 62°
d. 66°

Explanation:

Step1: Recall tangent - chord angle formula

The measure of a tangent - chord angle is half the measure of the intercepted arc.

Step2: Apply the formula

Let the measure of the intercepted arc $\widehat{DE}=132^{\circ}$. Let $\angle DEF$ be the tangent - chord angle. Then $\angle DEF=\frac{1}{2}\times\widehat{DE}$.
$\angle DEF=\frac{1}{2}\times132^{\circ}$

Answer:

D. $66^{\circ}$