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°