ABCDE is a regular pentagon. Its sides are extended as shown in the figure. The value of $\frac{∠ABC+2∠EGD+3∠BAJ}{6}$ is :
Answer & explanation
Correct answer: option 4
We know that,
Sum of two angles forming a linear pair = 180°.
Sum of interior angles of triangle = 180°.
If the side = n
Each angle = {(n - 2) × 180°}/n
Each interior angle of the regular pentagon ABCDE = {(n - 2) × 180°}/n
= {(5 - 2) × 180°}/5
= {3 × 180°}/5 = 108°
= ∠ABC = 108°
= ∠BAE = 108° ----(a)
= ∠BAJ + ∠BAE = 180° (Sum of two angles forming a linear pair is 180°)
= ∠BAJ + 108° = 180°
= ∠BAJ = 72° ----(b)
Similarly,
= ∠GED = 72°, ∠GDE = 72°
= ∠GED + ∠GDE + ∠EGD = 180°
= ∠EGD = 36° ----(c)
From (a), (b) and (c),
= (∠ABC + 2∠EGD + 3∠BAJ)/6
= (108° + 2 × 36° + 3 × 72°)/6 = 66°