Question

select the correct answer. in the figure, angle e measures 30°, angle f measures 57°, and angle b measures 27°. what is the measurement of angle a? a. 27° b. 66° c. 87° d. 93°

Explanation:

Step1: Find angle EBF in triangle BEF.

Sum of angles in $\triangle BEF$ is $180^{\circ}$. So $\angle EBF=180^{\circ}-30^{\circ}-57^{\circ}=93^{\circ}$.

Step2: Find angle A in triangle ABC.

$\angle ABC = 27^{\circ}$, so $\angle A=180^{\circ}-(93^{\circ}-27^{\circ}) - 90^{\circ}=66^{\circ}$.

Answer:

B. 66°