Question

(1) In ???? PQRS, m∠P = m∠R = 108°, m∠Q = m∠S = 72°. State which pair of sides of those given below is parallel.
(A) Side PQ and side QR (B) side PQ and side SR
(C) side SR and side SP (D) side PS and side PQ

Answer 1

if a quadirateral PQRS is given in such a way that ∠P = ∠R and ∠Q = ∠S
also ∠P + ∠Q = 180° , ∠P + ∠S = 180°
∠R + ∠Q = 180° , ∠R + ∠S = 180°
then, PQ || RS and PS || QR.

in given option , (A) is wrong because PQ doesn't parallel to QR
(B) is correct because PQ parallel to SR
(C) is wrong because SR doesn't parallel to SP.
(D) is wrong because PS doesn't parallel to P.

Answer 2

According to the problem given ,

In PQRS Quadrilateral ,

i ) m<P = m<R = 108°

ii ) m<Q = m<S = 72°

[ Opposite angles are equal . ]

iii ) m<P + m<Q =108+72 = 180°

Similarly , Sum of all adjecent angles are

supplementary .

Therefore ,

PQRS is a parallelogram.

PQ // SR

PS // QR

Option ( B ) is true.

I hope this helps you.

: )