In the given figure, O is center of the circle and OABC is a rhombus, then :

1. x° + y° = 180°

2. x° = y° = 90°

3. x° + 2y° = 360°

4. x° = y° = 45°

Join OB.

From figure,

OB = OA (Radius of same circle) ……..(1)

We know that,

Sides of rhombus are equal.

∴ OA = AB ………….(2)

From (1) and (2), we get :

⇒ OA = OB = AB

∴ OAB is an equilateral triangle.

Since, diagonals of rhombus bisect the interior angles.

In △OAB,

∠AOB = $\dfrac{x}{2}$

∠OBA = $\dfrac{y}{2}$

Since, each angle of equilateral triangle is 60°.

∴ ∠AOB = 60°

⇒ $\dfrac{x}{2} = 60°$

⇒ x = 120°.

∴ ∠OBA = 60°

⇒ $\dfrac{y}{2} = 60°$

⇒ y = 120°.

Substituting value of x and y in L.H.S. of equation x° + 2y° = 360°, we get :

⇒ 120° + 2(120°)

⇒ 120° + 240°

⇒ 360°.

Since, L.H.S. = R.H.S.

Hence, Option 3 is the correct option.