Question

multiple choice 1 point
what is the measure of ∠cbf?
128°
136°
98°
90°

Explanation:

Step1: Recall angle - sum property on a straight - line

The sum of angles on a straight - line is 180°. $\angle CBA = 180^{\circ}$.

Step2: Identify known angles

We know that $\angle CBA=\angle CBD+\angle DBE+\angle EBF+\angle FBA$, where $\angle FBA = 44^{\circ}$ and $\angle CBD = 52^{\circ}$ and $\angle DBE = 46^{\circ}$.

Step3: Calculate $\angle CBF$

$\angle CBF=\angle CBD+\angle DBE+\angle EBF$. Since $\angle CBA = 180^{\circ}$, and we want to find $\angle CBF$, and we know $\angle FBA = 44^{\circ}$, then $\angle CBF=180^{\circ}-\angle FBA$.
$\angle CBF = 180 - 44=136^{\circ}$.

Answer:

$136^{\circ}$ (corresponding to the second option in the multiple - choice list)