Question

Can someone please help me with this ​

Answer 1

59°

Explanation:

In a parallelogram, opposite angles are equal.

m∠PSR = m∠PQR

⇒ 7x° – 5° = 6x° + 13°

⇒ 7x° – 6x° = 13° + 5°

⇒ x° = 18°

Therefore, m∠PSR = 7(18°) – 5° = 121°

In a parallelogram, sum of the adjacent angles is 180°.

So, m∠QPS + m∠PSR = 180°

⇒ m∠QPS + 121° = 180°

⇒ m∠QPS = 180° – 121°

⇒ m∠QPS = 59°

Hence, m∠QPS must be 59° for PQRS to be a parallelogram.