Question

find the measure of angle abf. * 1 point 114° b a c d f e

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. Angle $\angle ABC$ and the given $114^{\circ}$ angle are vertical angles, so $\angle ABC = 114^{\circ}$.

Step2: Use linear - pair property

$\angle ABC$ and $\angle ABF$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. Let $\angle ABF=x$. Then $x + \angle ABC=180^{\circ}$.

Step3: Substitute and solve

Substitute $\angle ABC = 114^{\circ}$ into the equation $x+\angle ABC = 180^{\circ}$. We get $x+114^{\circ}=180^{\circ}$. Solving for $x$, we have $x=180^{\circ}-114^{\circ}=66^{\circ}$.

Answer:

$66^{\circ}$