Question

find the measure of angle ebf.

Explanation:

Step1: Note vertical - angle relationship

Vertical angles are equal. Angle $\angle ABC$ and the angle opposite to it are vertical angles. So, $\angle ABC = 114^{\circ}$.

Step2: Use right - angle information

We know that $\angle ABE=90^{\circ}$ (right - angle).

Step3: Calculate $\angle EBF$

$\angle ABC=\angle ABE+\angle EBF$. So, $\angle EBF=\angle ABC - \angle ABE$. Substitute $\angle ABC = 114^{\circ}$ and $\angle ABE = 90^{\circ}$ into the formula: $\angle EBF=114^{\circ}-90^{\circ}=24^{\circ}$.

Answer:

$24^{\circ}$