Question

Find x and y in the parallelogram PQRS.

Answer 1

Given:

PQRS is a parallelogram

Angles at point P:

∠SPR = x + 12°

∠QPR = 56°

∠PRS = 2x + 8°

Need to find x and then y = ∠PQR

Step 1: Use Triangle Angle Sum Property in △PRS

In triangle PRS, the sum of the interior angles is ∠SPR + ∠PRS + ∠QPR = 180°

Substitute:

(x + 12) + (2x + 8) + 56 = 180

3x + 76 = 180

3x = 104

⇒ x = 24°

Step 2: Find y = ∠PQR

In parallelogram PQRS, opposite angles are equal and adjacent angles are supplementary.

From the diagram:

Total angle at point P:

∠SPR + ∠QPR

= (x + 12) + 56

= 24 + 12 + 56

= 92°

So, adjacent angle

∠PQR = y

= 180° – 92°

= 88°