Question

In a rhombus PQRS if PQ = 7.5 cm then find the length of QR. If $\angle QPS={75}^{\circ }$ then find the measure of $\angle PQR\text{and}\angle SRQ.$

Answer 1

All the sides of a rhombus are equal.

So, PQ = QR = 7.5 cm
A rhombus is also a parallelogram so,
$\angle QPS=\angle SRQ={75}^{\circ }$ (opposite angles of a parallelogram are congruent)
$\text{Also,}\angle QPS+\angle PQR={180}^{\circ }$ (interior angles on the same side of the transversal are supplementary)
$\Rightarrow {75}^{\circ }+\angle PQR={180}^{\circ }$
$\Rightarrow \angle PQR={105}^{\circ }$