Question

given that ray xz bisects <wxy, find the measurement of the angles. m<yxz = m<yxw =

Explanation:

Step1: Recall angle - bisector property

An angle - bisector divides an angle into two equal angles. Since ray $XZ$ bisects $\angle WXY$, then $\angle WXZ=\angle YXZ$.

Step2: Determine $\angle YXZ$

Given that $\angle WXZ = 57^{\circ}$, so $\angle YXZ=57^{\circ}$ because of the angle - bisector property.

Step3: Calculate $\angle YXW$

$\angle YXW=\angle WXZ+\angle YXZ$. Since $\angle WXZ = \angle YXZ=57^{\circ}$, then $\angle YXW=57^{\circ}+57^{\circ}=114^{\circ}$.

Answer:

$m\angle YXZ = 57^{\circ}$
$m\angle YXW = 114^{\circ}$