Question

In a parallelogram PQRS, if P = (3x - 5)o and Q = (2x +15)o. Find the value of x.​

Answer 1

(Diagram is given in attachment)

Concept used:

→ In a parallelogram, 2 adjacent sides sum up to 180°

→ Opposite sides are parallel in a parallelogram.

→ All angles are equal in a parallelogram.

Solution:

In the figure,

➥ ∠QPS + ∠PQR = 180°

↦ (3x - 5)° + (2x + 15)° = 180°

➜ 3x + 2x + 15 - 5 = 180°

➞ 5x + 10 = 180°

➝ 5x = 180° - 10°

➝ 5x = 170°

➝ x = 170 ÷ 5

➝ x = 34°

∴ Value of x is 34°

Now, for finding the angles,

• ∠QPS

∠QPS = (3x - 5)°

∠QPS = 3(34) - 5

∠QPS = 97°

• ∠PQR

∠PQR = (2x + 15)°

∠PQR = 2(34) + 15

∠PQR = 83°