Question

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

Answer 1

All the sides of a rhombus are equal. 

So, PQ=QR=7.5 cm 

A rhombus is also a parallelogram so, 

∠QPS=∠SRQ=75^o 

(opposite angles of a parallelogram are congruent) 

Also, ∠QPS+∠PQR=180^o 

(interior angles on the same side of the transversal are supplementary) 

⇒75^o +∠PQR=180^o 

⇒∠PQR=105^o