Question

2a. sally constructed ∠aob with \overrightarrow{oc} as an angle bisector of ∠aob. if the measure of ∠aob is 84 degrees, what is the measure of ∠aoc?

Explanation:

Step1: Recall angle bisector definition

An angle bisector divides an angle into two equal parts. So, \( \angle AOC=\angle BOC \), and \( \angle AOB = \angle AOC+\angle BOC \).

Step2: Substitute and solve

Since \( \angle AOC=\angle BOC \), we can write \( \angle AOB = 2\angle AOC \). Given \( \angle AOB = 84^\circ \), then \( \angle AOC=\frac{\angle AOB}{2} \). Substituting the value, we get \( \angle AOC=\frac{84^\circ}{2} = 42^\circ \).

Answer:

\( 42 \) degrees