The ratio of the angles ∠A and ∠B of the rhombus ABCD is 1 ∶ 3. Find the value of ∠D.

Option 1 : 135°

**Given:**

∠A ∶ ∠B = 1 ∶ 3

**Concept Used:**

The opposite angles of a rhombus are equal.

The Sum of all angles in a quadrilateral is 360°.

**Calculation:**

Let assume that ∠A be x and ∠B be 3x

⇒ ∠B = ∠D = 3x

⇒ ∠A = ∠C = x

⇒ ∠A + ∠B + ∠C + ∠D = 360°

⇒ x + 3x + x + 3x = 360°

⇒ 8x = 360°

⇒ x = 45°

∠D = 3x

⇒ 3 × 45°

⇒ 135°

**∴**** The value of ****∠D**** is 135°. **