Question

In a rhombus PQRS if PQ = 7.5 then find QR. If $\angle$QPS = ${75}^{°}$ then find the measure of $\angle$PQR 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 = ${75}^{°}$ (opposite angles of a parallelogram are congruent)
Also, $\angle$QPS + $\angle$PQR = $180°$ (interior angles on the same side of the transversal are supplementary)
$$\begin{gathered} \Rightarrow 75°+\angle \mathrm{PQR}=180° \\ \Rightarrow \angle \mathrm{PQR}=105° \end{gathered}$$