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?
Answer & explanation
Correct answer: option 4
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°