Question

in the figure below, m∠ebd = 23°, bc bisects ∠abd, and be bisects ∠cbd. find m∠abc.

Explanation:

Step1: Use the angle - bisector property

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

Step2: Use the angle - bisector property again

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

Answer:

$46$