Question

in the figure below, ray \\( \overrightarrow { w y } \\) bisects \\( \angle x w z \\), and \\( \angle y w z = 35 ^ { \circ } \\). what is the value of a?
\\( \mathbf { a } \\) 20
\\( \mathbf { b } \\) 25
\\( \mathbf { c } \\) 35
\\( \mathbf { d } \\) 50

Explanation:

Step1: Recall the definition of an angle - bisector

An angle - bisector divides an angle into two equal parts. Since ray \(\overrightarrow{WY}\) bisects \(\angle XWZ\), we have \(\angle XWY=\angle YWZ\).

Step2: Substitute the given value

We are given that \(\angle YWZ = 35^{\circ}\). By the angle - bisector property \(\angle XWY=a^{\circ}\) and \(a = \angle YWZ\).

Answer:

C. \(35\)