Question

in the figure below, m∠abd = 82°, m∠cbd = 56°, and (overline{be}) bisects ∠cbd. find m∠abe. m∠abe = (square^{circ})

Explanation:

Step1: Find the measure of ∠CBE

Since $\overline{BE}$ bisects $\angle CBD$ and $m\angle CBD = 56^{\circ}$, then $m\angle CBE=\frac{1}{2}m\angle CBD$. So $m\angle CBE=\frac{1}{2}\times56^{\circ}=28^{\circ}$.

Step2: Find the measure of ∠ABE

We know that $m\angle ABE=m\angle ABD - m\angle EBD$. Also, $m\angle EBD = m\angle CBE$. So $m\angle ABE=m\angle ABD - m\angle CBE$. Substituting the given values, $m\angle ABD = 82^{\circ}$ and $m\angle CBE = 28^{\circ}$, we get $m\angle ABE=82^{\circ}- 28^{\circ}=54^{\circ}$.

Answer:

$54$