Question

In a rhombus PQRS, ∠P = (4x – 10)° and ∠R = (3x + 20)°. Find the values of x and ∠Q.

Answer 1

Given,

In a rhombus PQRS, ∠P = (4x – 10)° and ∠R = (3x + 20)°.

The opposite angles of a rhombus are equal and the opposite sides are also equal,

⇒ ∠P = ∠R

⇒ 4x – 10 = 3x + 20

⇒ 4x – 3x = 20 + 10

⇒ x = 30°

The sum of the adjacent sides of a parallelogram is linear,

⇒ ∠P + ∠Q = 180°

⇒ 4x – 10° + ∠Q = 180°

⇒ ∠Q = 180° + 10° – 120°

⇒ ∠Q = 190° – 120° = 70°

Hence, this is required.