Question

In parallelogram PQRS, ∠P = (9x – 5)° and ∠Q = (4x – 10)°. Find the values of x and ∠R.

Answer 1

In parallelogram PQRS, ∠P = (9x – 5)° and ∠Q = (4x – 10)°

We know the measure of a straight angle is 180°

⇒ ∠P + ∠Q = 180°

⇒ 9x – 5 + 4x – 10 = 180°

⇒ 13x = 180° + 15° 

⇒ 13x = 195°

⇒ x = 15°

The opposite sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

And ∠P = 9x – 5 = 9 × 15 – 5

⇒ 9 × 15 – 5 = 135 – 5 = 130° = ∠R

Hence, this is required.