Question

in the figure below, ray \\( \overrightarrow { w y } \\) bisects \\( \angle x w z \\). what is the value of \\( a \\)?

Explanation:

Step1: Use the angle - bisector property

Since ray \(\overrightarrow{WY}\) bisects \(\angle XWZ\), then \(\angle XWY=\angle YWZ = a^{\circ}\).

Step2: Set up an equation based on the sum of angles around a point

The sum of angles around a point is \(360^{\circ}\). But if we consider the non - overlapping angles at point \(W\) related to the given bisected angles, we know that \(a + a+4a=180\) (assuming the figure is a straight - line related angle situation, as the sum of adjacent angles forming a linear pair or a semi - circular arc is \(180^{\circ}\)).
Simplify the left - hand side of the equation: \(6a = 180\).

Step3: Solve for \(a\)

Divide both sides of the equation \(6a=180\) by \(6\): \(a=\frac{180}{6}\).

Answer:

\(a = 30\), so the answer is A. 30