Question

in the figure below, m∠abd = 104°, m∠ebd = 34°, and (overline{be}) bisects ∠cbd. find m∠abc.

Explanation:

Step1: Find m∠CBD

Since $\overline{BE}$ bisects $\angle CBD$ and $m\angle EBD = 34^{\circ}$, then $m\angle CBD=2\times m\angle EBD$.
$m\angle CBD = 2\times34^{\circ}=68^{\circ}$

Step2: Find m∠ABC

We know that $m\angle ABD=m\angle ABC + m\angle CBD$. So, $m\angle ABC=m\angle ABD - m\angle CBD$.
$m\angle ABC=104^{\circ}- 68^{\circ}=36^{\circ}$

Answer:

$36$