Question

in the figure below, (mangle ebd = 28^{circ}), (overline{bc}) bisects (angle abd), and (overline{be}) bisects (angle cbd). find (mangle abc).

Explanation:

Step1: Use angle - bisector property

Since $\overline{BE}$ bisects $\angle CBD$, then $m\angle CBD = 2m\angle EBD$. Given $m\angle EBD=28^{\circ}$, so $m\angle CBD = 2\times28^{\circ}=56^{\circ}$.

Step2: Use angle - bisector property again

Since $\overline{BC}$ bisects $\angle ABD$, then $m\angle ABC=m\angle CBD$.

Answer:

$56$