Question

question 4 of 10 the measure of $widehat{de}$ is 108°. what is the measure of $angle def$, the tangent - chord angle? a. 108° b. 216° c. 58° d. 54°

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

Given the intercepted arc $\overparen{DE}$ has a measure of $108^{\circ}$. Let $\angle DEF$ be the tangent - chord angle. Then $\angle DEF=\frac{1}{2}\times m\overparen{DE}$.

Step3: Calculate the angle measure

$\angle DEF=\frac{1}{2}\times108^{\circ} = 54^{\circ}$.

Answer:

D. 54°