Question

1. in the figure below, $overrightarrow{cd}$ intersects $overrightarrow{ef}$ at point b. what is the measure of angle c? a. 31° b. 47° c. 71° d. 133°

Explanation:

Step1: Identify vertical - angles

$\angle EBC$ and the $31^{\circ}$ angle are vertical - angles, so $\angle EBC = 31^{\circ}$.

Step2: Use triangle - angle sum property

In $\triangle EBC$, the sum of interior angles is $180^{\circ}$. Let $\angle C=x$, $\angle E = 102^{\circ}$, and $\angle EBC = 31^{\circ}$. Then $x+102^{\circ}+31^{\circ}=180^{\circ}$.

Step3: Solve for $\angle C$

$x=180^{\circ}-(102^{\circ}+31^{\circ})=180^{\circ}-133^{\circ}=47^{\circ}$.

Answer:

B. $47^{\circ}$