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

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

(a) 72 °

(b) 36 °

(c) 60 °

(d) 54 °

Sol:

Given: 

Sides of pentagon BA and DE extended to meet at F. 

Concept used:  S

Sum of interior angles of a regular pentagon is 540°. 

Each interior angle = 180(n – 2)/n 

Where, n =  number of sides  Sum of all angles in a triangle is 180°. 

Sum of angles of a straight line is 180°.

BA extended up to F.

 DE extended up to F. 

Each interior angle of the pentagon = 180(5 – 2)/5 

Each interior angle of the pentagon = 108°  

Each angle of a regular pentagon is 108°. 

BF forms a straight line. 

⇒ ∠BAE + ∠EAF = 180° 

⇒ ∠EAF = 180° – 108° 

⇒ ∠EAF = 72°

DF forms a straight line. 

⇒ ∠DEA + ∠AEF = 180° 

⇒ ∠AEF = 180° – 108° 

⇒ ∠AEF = 72°  In ΔAEF 

⇒ ∠AEF + ∠EAF + ∠EFA = 180° 

⇒ ∠EFA = 180° – 72° – 72° 

⇒ ∠EFA = 36°