Question

question 18 of 25
if \\( \angle a v b \\) has a measure of \\( 80^{circ} \\) and \\( \overline{v m} \\) is its angle bisector, what is the measure of \\( \angle a v m \\)?

a. \\( 80^{circ} \\)
b. \\( 160^{circ} \\)
c. \\( 20^{circ} \\)
d. \\( 40^{circ} \\)

Explanation:

Step1: Recall the definition of an angle bisector

An angle bisector divides an angle into two equal parts.

Step2: Calculate the measure of ∠AVM

Since \( \angle AVB = 80^{\circ}\) and \(VM\) is the angle bisector of \( \angle AVB\), then \( \angle AVM=\frac{1}{2}\angle AVB\).
Substitute \( \angle AVB = 80^{\circ}\) into the formula: \( \angle AVM=\frac{1}{2}\times80^{\circ}\).

$$ \angle AVM = 40^{\circ} $$

Answer:

D. \(40^{\circ}\)