Question

problems 3 - 5: determine the measure of each angle in the diagram. explain your thinking.

1. ∠abc
2. ∠ebd
3. ∠abe

Explanation:

Step1: Identify vertical - angle relationship

$\angle ABC$ and the $50^{\circ}$ angle are vertical angles. Vertical angles are equal.

Step2: Determine $\angle ABC$ measure

$\angle ABC = 50^{\circ}$

Step3: Identify $\angle EBD$ relationship

$\angle EBD$ and the $50^{\circ}$ angle are also vertical angles.

Step4: Determine $\angle EBD$ measure

$\angle EBD=50^{\circ}$

Step5: Identify $\angle ABE$ relationship

$\angle ABE$ and $\angle ABC$ form a straight - line, so $\angle ABE+\angle ABC = 180^{\circ}$ (linear - pair of angles).

Step6: Calculate $\angle ABE$ measure

$\angle ABE=180^{\circ}-\angle ABC$. Since $\angle ABC = 50^{\circ}$, then $\angle ABE = 180 - 50=130^{\circ}$

Answer:

1. $\angle ABC = 50^{\circ}$
2. $\angle EBD = 50^{\circ}$
3. $\angle ABE=130^{\circ}$