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

 = 75We know that rhombus is a parallelogram with a pair of adjacent sides equal.

Here , PQRS is a rhombus.

Hence, adjacent sides PQ and QR are equal.

So,PQ =QR = 7.5 cm.

Now, 
draw diagonal PR

we have, PQ=QR and ∠QPS = 75º
triangle PQR is isosceles
∠QPS = 75°

So, ∠SRQ  = 75° (opposite angles of a rhombus are equal in measure)
∠PQR=(180-75-75)/2= 15° {Adjacent sides (ones next to each other) of a rhombus are supplementary. This means that their measures add up to 180 degrees.}