Question

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