ABCDE is a regular pentagon.  Its sides are extended as shown in the figure.  The value of \(\frac{∠ABC\;+\;5∠EGD\;+\;2.5∠BAJ}{9}\)is?

52°

In Pentagon ABCDE

Interior angle = \(\frac{180\;×\;(n\;-\;2)}{n}\)

\(\frac{180\;×\;(5\;-\;2)}{5}\) = 108°

⇒ Interior angle = ∠ABC = ∠BAE = 108°

⇒ ∠BAJ = 180° - ∠BAE = 180° - 108° = 72°

⇒ ∠GED = ∠GDE = 72°

⇒ ∠EGD = 180° - (72° + 72°) = 36°

Now, ATQ,

⇒ \(\frac{∠ABC\;+\;5∠EGD\;+\;2.5∠BAJ}{9}\)

= \(\frac{108°\;+\;(5\;×\;36°)\;+\;(2.5\;×\;72)}{9}\)

= 52°