Question

In the given figure, O is the centre of a circle. AB is the side of a square and BC is side of a regular hexagon. Also, arc AD = arc CD. Angle DOC is equal to:

Options

• 150°

• 105°

• 130°

• 210°

Answer 1

105°

Explanation:

Since, AB is the side of square.

∴ ∠AOB = `(360°)/4`​ = 90°

Since, BC is the side of regular hexagon.

∴ ∠BOC = `(360°)/6`​ = 60°

We know that,

Equal arcs subtends equal angles at the center.

Since, arc AD = arc CD

∴ ∠AOD = ∠COD = x (let)

From figure,

⇒ ∠AOD + ∠COD + ∠AOB + ∠BOC = 360°

⇒ x + x + 90° + 60° = 360°

⇒ 2x + 150° = 360°

⇒ 2x = 360° − 150°

⇒ 2x = 210°

⇒ x = `(210°)/2` = 105°