Question

question 9 of 10
if the measure of \\( \angle def \\) is \\( 76 ^ { \circ } \\), what is the measure of \\( \widehat { d e } \\) ?

Explanation:

Step1: Recall the tangent - secant angle formula

The measure of an angle formed by a tangent and a secant is half the measure of the intercepted arc. The formula is \(m\angle DEF=\frac{1}{2}m\overarc{DE}\).

Step2: Solve for \(m\overarc{DE}\)

Given \(m\angle DEF = 76^{\circ}\), we can rewrite the formula from Step 1 as \(m\overarc{DE}=2\times m\angle DEF\).
Substitute \(m\angle DEF = 76^{\circ}\) into the equation: \(m\overarc{DE}=2\times76^{\circ}\).

Answer:

\(152^{\circ}\), so the answer is C.