Question

In the given figure, AB is the side of regular pentagon and BC is the side of regular hexagon. Angle APC is:

पर्याय

• 132°

• 66°

• 90°

• 120°

Answer 1

66°

Explanation: 

Since,

AB is the side of regular pentagon.

∴ ∠AOB = `(360°)/5` = 72°

BC is the side of regular hexagon.

∴ ∠BOC = `(360°)/6`​ = 60°

From figure,

∠AOC = ∠AOB + ∠BOC = 72° + 60° = 132°

We know that,

The angle which an arc of a circle subtends at the center is double that which it subtends at any point on the remaining part of the circumference.

⇒ ∠AOC = 2∠APC

⇒ ∠APC = `(∠AOC)/2 = (132°)/2​` = 66°