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 :

66°

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°