Question

problems 3 - 5 determine the measure of each angle in the diagram. angle measure (degrees) ∠abc ∠ebd ∠abe explain your thinking.

Explanation:

Step1: Identify vertical - angles

Vertical angles are equal. $\angle ABC$ and the given $50^{\circ}$ angle are vertical - angles. So, $\angle ABC = 50^{\circ}$.

Step2: Identify vertical - angles for $\angle EBD$

$\angle EBD$ and the given $50^{\circ}$ angle are also vertical - angles. So, $\angle EBD=50^{\circ}$.

Step3: Use linear - pair property for $\angle ABE$

$\angle ABE$ and $\angle EBD$ form a linear pair. A linear pair of angles sums to $180^{\circ}$. Let $\angle ABE = x$. Then $x+\angle EBD = 180^{\circ}$. Since $\angle EBD = 50^{\circ}$, we have $x=180 - 50=130^{\circ}$.

Answer:

Angle	Measure (degrees)
$\angle EBD$	$50$
$\angle ABE$	$130$