Question

angle abc is a straight angle. ( mangle dbc = 130^{circ} ) and (overrightarrow{be}) bisects (angle abd). what is ( mangle eba )?

Explanation:

Step1: Find the measure of $\angle ABD$

Since $\angle ABC$ is a straight angle ($180^{\circ}$) and $\angle DBC = 130^{\circ}$, we use the formula $\angle ABD=\angle ABC-\angle DBC$.
So, $\angle ABD = 180^{\circ}- 130^{\circ}=50^{\circ}$.

Step2: Use the angle - bisector property

Because $\overrightarrow{BE}$ bisects $\angle ABD$, by the definition of an angle bisector ($\angle EBA=\frac{1}{2}\angle ABD$).
Substitute $\angle ABD = 50^{\circ}$ into the formula: $\angle EBA=\frac{1}{2}\times50^{\circ}=25^{\circ}$.

Answer:

$25$