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Question
In a rhombus PQRS if PQ = 7.5 cm then find QR. If ∠QPS = 75° then find the measure of ∠PQR and ∠SRQ.
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Solution
PQ = 7.5 cm ...[Given]
`square`PQRS is a rhombus. ...[Given]
∴ QR = PQ ...[Sides of a rhombus are congruent]
∴ QR = 7.5 cm
∠QPS = 75° ...[Given]
∠QPS + ∠PQR = 180° ...[Adjacent angles of a rhombus are supplementary]
∴ 75° + ∠PQR = 180°
∴ ∠PQR = 180° – 75°
∴ ∠PQR = 105°
∠SRQ = ∠QPS ...[Opposite angles of a rhombus]
∴ ∠SRQ = 75°
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