SSC CHSL 2020 PYQ — Question 61

ABCDE is a regular pentagon.

Each angle of a regular pentagon = [(n - 2)180⁰]/n = [(5 - 2)180⁰]/5 = 108⁰

∠ABC = ∠BCD = ∠CDE = ∠ DEA  = ∠EAB = 108⁰

From the figure,

∠BAJ + ∠EAB = 180⁰

∠BAJ + 108⁰ = 180⁰

∠BAJ = 72⁰

∠DEA + ∠GED = 180⁰

∠GED = 180⁰ - 108⁰

∠GED = 72⁰

∠CDE + ∠GDE = 180⁰

∠GDE = 72⁰

In triangle GED -

∠GDE + ∠GED + ∠EGD = 180⁰

72⁰ + 72⁰ + ∠EGD = 180⁰

∠EGD = 36⁰

Thus,

= (∠ABC + 2∠EGD + 3∠BAJ)/6 

= (108⁰ + 2(36⁰) + 3(72⁰))/6

= (108⁰ + 72⁰ + 216⁰)/6

= (396⁰)/6

= 66⁰