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.
