Question

given that ray xz bisects <wxy, find the measurement of the angles.
w
39°
z
x
y
m<zxy =
type your answer.
m<wxy =
type your answer.

Explanation:

Step1: Recall angle - bisector property

A ray that bisects an angle divides the angle into two equal angles. Given that $\overrightarrow{XZ}$ bisects $\angle WXY$, then $\angle WXZ=\angle ZXY$.

Step2: Find $\angle ZXY$

Since $\angle WXZ = 39^{\circ}$ and $\angle WXZ=\angle ZXY$, then $m\angle ZXY=39^{\circ}$.

Step3: Find $\angle WXY$

The measure of $\angle WXY$ is the sum of $\angle WXZ$ and $\angle ZXY$. Since $\angle WXZ=\angle ZXY = 39^{\circ}$, then $m\angle WXY=m\angle WXZ + m\angle ZXY=39^{\circ}+39^{\circ}=78^{\circ}$.

Answer:

$m\angle ZXY = 39^{\circ}$
$m\angle WXY = 78^{\circ}$