Question

In the parallelogram PQRS, ∠P = 128° and ∠QSR = 36°. Find x.

Answer 1

Given:

• PQRS is a parallelogram.
• ∠P = 128°
• ∠QSR = 36°
• Need to find x = ∠PQR (marked on the figure).

Step wise calculation:

1. Opposite angles of a parallelogram are equal, so ∠R = ∠P = 128°.

2. Adjacent angles in a parallelogram are supplementary, so: ∠P + ∠S = 180°

128° + ∠S = 180°

⇒ ∠S = 52°

3. In triangle QSR: The angles are ∠QSR = 36°, ∠QRS = x and ∠SQR.

4. Since PQRS is a parallelogram, PS || QR, so alternate interior angles are equal.

Hence, ∠SQR = ∠P = 128°.

5. Sum of internal angles of triangle QSR = 180°

∠QSR + ∠QRS + ∠SQR = 180°

36° + x + 128° = 180°

⇒ x + 164° = 180°

⇒ x = 180° – 164° = 16°