Question

in the figure below, m∠abd = 96°, m∠ebd = 27°, and be bisects ∠cbd. find m∠abc.

Explanation:

Step1: Find m∠CBD

Since $\overline{BE}$ bisects $\angle CBD$, then $m\angle CBD = 2\times m\angle EBD$. Given $m\angle EBD=27^{\circ}$, so $m\angle CBD = 2\times27^{\circ}=54^{\circ}$.

Step2: Find m∠ABC

We know that $m\angle ABD=m\angle ABC + m\angle CBD$. So $m\angle ABC=m\angle ABD - m\angle CBD$. Given $m\angle ABD = 96^{\circ}$ and $m\angle CBD = 54^{\circ}$, then $m\angle ABC=96^{\circ}-54^{\circ}=42^{\circ}$.

Answer:

$42$