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

Solution (By Examveda Team)

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