Question

YA is the angle bisector of ZXYZ. If mZXYZ = 52°, what is mZZYA?

Answer 1

Given:

$YA$ is the angle bisector of $\angle XYZ$.

$m\angle XYZ=52^\circ$

To find:

The measure of $m\angle ZYA$.

Solution:

It is given that $YA$ is the angle bisector of $\angle XYZ$. It means

$m\angle XYA=m\angle ZYA$            ...(i)

Now,

$m\angle XYA+m\angle ZYA=m\angle XYZ$

$m\angle ZYA+m\angle ZYA=52^\circ$            [Using (i)]

$2m\angle ZYA=52^\circ$

Divide both sides by 2.

$m\angle ZYA=\dfrac{52^\circ}{2}$

$m\angle ZYA=26^\circ$

Therefore, the required value is $m\angle ZYA=26^\circ$.