Question

Q.3. In a rhombus PQRS, if PQ = 7.5 then find QR. If LQPS = 75° then find
the measure of LPQR and ZSRQ.
​

Answer 1

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°

Answer 2

Step-by-step explanation:

All the sides of a rhombus are equal.

So, PQ = QR = 7.5 cm

A rhombus is also a parallelogram so,

ZQPS = LSRQ = 75° (opposite angles of a parallelogram are congruent)

Also, 2QPS + ZPQR = 180° (interior angles on the same side of the transversal are supplementary)

75° + ∆PQR = 180°

» LPQR = 105°