Question

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

विकल्प

• x° + y° = 180°

• x° = y° = 90°

• x° + 2y° = 360°

• x° = y° = 45°

Answer 1

x° + 2y° = 360°

Explanation:

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 = `x/2`

∠OBA = `y/2`

Since, each angle of equilateral triangle is 60°.

∴ ∠AOB = 60°

⇒ `x/2 = 60°`

⇒ x = 120°

∴ ∠OBA = 60°

⇒ `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.