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

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Solution

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

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