Question

use the diagram to find the measures of each angle. explain your reasoning.

Explanation:

Step1: Vertical - angle property

Vertical angles are equal. $\angle DBC = 50^{\circ}$, and its vertical - angle $\angle ABE=50^{\circ}$.

Step2: Supplementary - angle property

$\angle DBC$ and $\angle EBD$ are supplementary (a straight - line angle is $180^{\circ}$). So, $\angle EBD = 180^{\circ}-\angle DBC$.
$\angle EBD=180 - 50=130^{\circ}$.

Step3: Vertical - angle property for $\angle EBD$

The vertical - angle of $\angle EBD$ is $\angle ABC$, so $\angle ABC = 130^{\circ}$.

Answer:

$\angle ABE = 50^{\circ}$, $\angle ABC = 130^{\circ}$, $\angle EBD = 130^{\circ}$, $\angle DBC = 50^{\circ}$