Question

in the figure below, (mangle abd = 100^{circ},mangle ebd = 26^{circ}), and (overline{be}) bisects (angle cbd). find (mangle abc).

Explanation:

Step1: Find m∠CBD

Since $\overline{BE}$ bisects $\angle CBD$ and $m\angle EBD = 26^{\circ}$, then $m\angle CBD=2\times m\angle EBD$.
$m\angle CBD = 2\times26^{\circ}=52^{\circ}$

Step2: Find m∠ABC

We know that $m\angle ABD=m\angle ABC + m\angle CBD$. So, $m\angle ABC=m\angle ABD - m\angle CBD$.
$m\angle ABC=100^{\circ}- 52^{\circ}=48^{\circ}$

Answer:

$48$