Question

calculate
enter the unknown angle measures into the table.
angle angle measure
abc 68
cbd 68
dbe 68
abe 0.5
reset

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. $\angle ABC$ and $\angle DBE$ are vertical angles, $\angle CBD$ and $\angle ABE$ are vertical angles. Given $\angle ABC = 68^{\circ}$, so $\angle DBE=68^{\circ}$.

Step2: Use linear - pair property

Since $\angle ABC$ and $\angle CBD$ form a linear - pair, and the sum of angles in a linear - pair is $180^{\circ}$. Also, $\angle ABC = 68^{\circ}$, and $\angle ABC+\angle CBD = 180^{\circ}$, then $\angle CBD=180 - 68=112^{\circ}$. And $\angle ABE=\angle CBD = 112^{\circ}$ (vertical angles).

Answer:

Angle	Angle Measure
$CBD$	$112^{\circ}$
$DBE$	$68^{\circ}$
$ABE$	$112^{\circ}$