Question

1. if \\( \angle a o c = 48 ^ { \circ } \\) and \\( \angle b o c = 21 ^ { \circ } \\), find the measure of \\( \angle a o b \\).

a. \\( 24 ^ { \circ } \\)
b. \\( 32 ^ { \circ } \\)
c. \\( 27 ^ { \circ } \\)
d. \\( 29 ^ { \circ } \\)

Explanation:

Step1: Analyze the relationship between angles

From the figure, we know that \(\angle AOC=\angle AOB + \angle BOC\).

Step2: Solve for \(\angle AOB\)

Rearrange the formula to get \(\angle AOB=\angle AOC-\angle BOC\).
Substitute \(\angle AOC = 48^{\circ}\) and \(\angle BOC = 21^{\circ}\) into the formula: \(\angle AOB=48^{\circ}- 21^{\circ}\).
Calculate \(48 - 21=27\), so \(\angle AOB = 27^{\circ}\).

Answer:

C. \(27^{\circ}\)