Question

in the figure below, m∠abd = 107°, m∠ebd = 35°, and (overline{be}) bisects ∠cbd. find m∠abc. m∠abc = °

Explanation:

Step1: Find ∠CBD

Since $\overline{BE}$ bisects $\angle CBD$ and $m\angle EBD = 35^{\circ}$, then $m\angle CBD=2\times m\angle EBD$. So $m\angle CBD = 2\times35^{\circ}=70^{\circ}$.

Step2: Find ∠ABC

We know that $m\angle ABD=m\angle ABC + m\angle CBD$. So $m\angle ABC=m\angle ABD - m\angle CBD$. Substituting the given values, $m\angle ABC = 107^{\circ}-70^{\circ}=37^{\circ}$.

Answer:

$37$