Question

in the figure below, \\( \angle b a d = 40 ^ { \circ } \\) and ray \\( \overrightarrow { a c } \\) bisects \\( \angle b a d \\). what is the measure of angle \\( \angle b a c? \\)

Explanation:

Step1: Recall the angle - bisector definition

An angle bisector divides an angle into two equal parts. If ray \(\overrightarrow{AC}\) bisects \(\angle BAD\), then \(\angle BAC=\angle CAD\) and \(\angle BAD = \angle BAC+\angle CAD\).

Step2: Calculate \(\angle BAC\)

Since \(\angle BAD = 40^{\circ}\) and \(\angle BAC=\angle CAD\) (because \(AC\) bisects \(\angle BAD\)), we can use the formula \(\angle BAC=\frac{1}{2}\angle BAD\). Substitute \(\angle BAD = 40^{\circ}\) into the formula: \(\angle BAC=\frac{1}{2}\times40^{\circ}\).

Answer:

C. \(20^{\circ}\)