Question

in the figure below, m∠ebd = 23°. (overline{bc}) bisects ∠abd, and (overline{be}) bisects ∠cbd. find m∠abc. m∠abc = (square^{circ})

Explanation:

Step1: Use angle - bisector property

Since $\overline{BE}$ bisects $\angle CBD$, then $\angle CBD = 2\angle EBD$. Given $\angle EBD=23^{\circ}$, so $\angle CBD = 2\times23^{\circ}=46^{\circ}$.

Step2: Use angle - bisector property again

Since $\overline{BC}$ bisects $\angle ABD$, then $\angle ABC=\angle CBD$. And we found that $\angle CBD = 46^{\circ}$, so $\angle ABC = 46^{\circ}$.

Answer:

$46$