Question

question 2 of 10
the measure of \\( \overparen { d e } \\) is \\( 132 ^ { \circ } \\). what is the measure of \\( \angle d e f \\), the tangent - chord angle?
a. \\( 62 ^ { \circ } \\)
b. \\( 132 ^ { \circ } \\)
c. \\( 66 ^ { \circ } \\)
d. \\( 264 ^ { \circ } \\)

Explanation:

Step1: Recall the tangent - chord angle formula

The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.

Step2: Apply the formula

Given the measure of the intercepted arc \( \overset{\frown}{DE}=132^{\circ}\). Let \( \angle DEF\) be the tangent - chord angle. Then \( \angle DEF=\frac{1}{2}\times\overset{\frown}{DE}\).
Substitute \( \overset{\frown}{DE} = 132^{\circ}\) into the formula: \( \angle DEF=\frac{1}{2}\times132^{\circ}\).

$$ \angle DEF = 66^{\circ} $$

Answer:

C. \(66^{\circ}\)