Question

in the figure below, (mangle abd = 92^{circ},mangle cbd = 64^{circ}), and (overline{be}) bisects (angle cbd). find (mangle abe).

Explanation:

Step1: Find measure of ∠CBE

Since $\overline{BE}$ bisects $\angle CBD$ and $m\angle CBD = 64^{\circ}$, then $m\angle CBE=\frac{1}{2}m\angle CBD$. So $m\angle CBE=\frac{1}{2}\times64^{\circ}= 32^{\circ}$.

Step2: Find measure of ∠ABE

We know that $\angle ABE=\angle ABD-\angle EBD$. Also, $\angle EBD = \angle CBE = 32^{\circ}$ and $\angle ABD = 92^{\circ}$. So $m\angle ABE=m\angle ABD - m\angle EBD=92^{\circ}-32^{\circ}=60^{\circ}$.

Answer:

$60$