91Ó°ÊÓ

The given diagram is:

The angle bisector theorem states that if$\stackrel{↔}{BX}$ is the bisector of $∠ABC$, then$∠ABX=\frac{1}{2}∠ABC$ and $∠XBC=\frac{1}{2}∠ABC$.

Given that $\stackrel{↔}{XZ}$bisects$∠WXY$.

Therefore, by using the angle bisector theorem it is obtained that:

$∠WXZ=\frac{1}{2}∠WXY$and $∠ZXY=\frac{1}{2}∠WXY$.

Therefore, by using the above relation it can be obtained that $∠WXZ=∠ZXY$.

As$∠WXZ=∠6$ and $∠ZXY=∠7$, therefore it can be deduced that $∠6=∠7$.

As the angles∠6 and∠7have equal measure therefore the angles∠6 and∠7 are congruent angles.

That implies, $∠6â‰\dots ∠7$.

The given diagram is:

The angle bisector theorem states that if$\stackrel{↔}{BX}$ is the bisector of $∠ABC$, then$∠ABX=\frac{1}{2}∠ABC$ and $∠XBC=\frac{1}{2}∠ABC$.

The name of theorem that justifies the conclusion is angle bisector theorem.