In a rhombus PQRS if PQ = 7.5 then find QR. If ∠QPS = 75° then find the measure of ∠PQR and ∠SRQ.

Given quadrilateral is a rhombus.

⇒ all the sides are congruent /equal

⇒ PQ = QR = 7.5

Also ∠QPS = 75° (given)

⇒∠QPS = 75° (opposite angles are congruent)

But ∠QPS + ∠PQR = 180° (adjacent angles are supplementary)

⇒ ∠PQR = 105°

∴ ∠SRQ = 105° (opposite angles)