Question

in the figure below, (mangle abd = 104^{circ},overline{bc}) bisects (angle abd), and (overline{be}) bisects (angle cbd). find (mangle ebd).

Explanation:

Step1: Find measure of ∠CBD

Since $\overline{BC}$ bisects $\angle ABD$ and $m\angle ABD = 104^{\circ}$, then $m\angle CBD=\frac{1}{2}m\angle ABD$. So $m\angle CBD=\frac{1}{2}\times104^{\circ} = 52^{\circ}$.

Step2: Find measure of ∠EBD

Since $\overline{BE}$ bisects $\angle CBD$, then $m\angle EBD=\frac{1}{2}m\angle CBD$. Substituting $m\angle CBD = 52^{\circ}$, we get $m\angle EBD=\frac{1}{2}\times52^{\circ}=26^{\circ}$.

Answer:

$26$