In a circle with center at point O, chord AB is a side of a square and chord BC is a side of regular hexagon. Then angle AOC is equal to:

1. 120°

2. 150°

3. 90°

4. none of these

We know that,

The angle subtended by each side of an n-sided regular polygon at the center of circle = $\dfrac{360°}{n}$

Given, AB is the side of the square.

Angle subtended by each arm of the square at the center of the circle is $\dfrac{360°}{4}$ = 90°.

⇒ ∠AOB = 90°.

BC is the side of the hexagon.

Angle subtended by each arm of the hexagon at the center of the circle is $\dfrac{360°}{6}$ = 60°.

⇒ ∠BOC = 60°.

From figure,

∠AOC = ∠AOB + ∠BOC = 90° + 60° = 150°.

Hence, option 2 is the correct option.