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In a rhombus PQRS, if PQ = 7.5 cm, then find QR. If ∠QPS 75°, then find the measures of ∠PQR and ∠SRQ.

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i. PQ = 7.5 cm [Given] 

PQRS is a rhombus. [Given] 

∴ QR = PQ [Sides of a rhombus are congruent] 

∴ QR = 7.5 cm 

ii. ∠QPS = 75° [Given] 

∠QPS + ∠PQR = 180° [Adjacent angles of a rhombus are supplementary] 

∴ 75° + ∠PQR = 180° 

∴ ∠PQR = 180° – 75° 

∴ ∠PQR =105°

iii. ∠SRQ = ∠QPS [Opposite angles of a rhombus] 

∴ ∠SRQ = 75° 

∴ QR = 7.5 cm, ∠PQR = 105°, ∠SRQ = 75°

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