The sides BA and DE of a regular pentagon are produced to meet at F. What is the measure of ∠EFA?

Answer: Option B

Interior angle of a regular polygon
$$\begin{array}{rl}& =\frac{\left(n-2\right)\times {180}^{\circ }}{n}\\ & =\frac{\left(5-2\right)\times {180}^{\circ }}{5}\\ & =108^{\circ }\end{array}$$
∠DEA = ∠BAE = 108°
∠AEF = ∠EAF = 72°
In ΔEAF,
∠E + ∠A + ∠F = 180°
72 + 72 + ∠EFA = 180°
∠EFA = 36°