Question

angle abc is a straight angle. m∠dbc = 130° and be bisects ∠abd. what is m∠eba?

Explanation:

Step1: Find the measure of ∠ABD

Since ∠ABC is a straight angle ($m\angle ABC = 180^{\circ}$) and $m\angle DBC=130^{\circ}$, we use the angle - addition postulate $\angle ABC=\angle ABD+\angle DBC$.
So, $m\angle ABD = 180^{\circ}-m\angle DBC$.
Substitute $m\angle DBC = 130^{\circ}$ into the formula: $m\angle ABD=180 - 130=50^{\circ}$.

Step2: Use the angle - bisector definition

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

Answer:

$25$