Question

PQRS is a kite. Q lines on AB such that PR is parallel to AB if angle PQA is equal to 20 degree and Angle BQR is equal to 30 degree find angle PSR, angle SPQ and angle SRQ

Answer 1

so I wrote one answer for your questions .And I think it is correct

Answer 2

Angle SRQ measures 60°

Since PS = PQ and RS = RQ

∠PSO = ∠PQO

∠RSO = ∠RQO

∠PSO + ∠RSO = ∠PQO + ∠RQO

∠PSR = ∠PQR

∠PQR = 180 - PQA+RQB ( As the sum of angles made on the same straight line is 180)

= 180 - 20+30

= 180-50

= 130°

Therefore, ∠PSR = 130

∠OPQ = ∠PQA = 20 ( Alternate interior angles)

∠POQ = 90 ( As diagnols of the kite intersect at right angle)

∠PQO = 180 - 20 + 90

∠PQO = 70

Thus, ∠PSO = ∠PQO = 70

In Δ POS

∠SPO = 180 - 90 + 70  

= 20

∠SPQ = ∠SPO + ∠OPQ

= 20 + 20

= 40

∠SRQ = 360 - SPQ + PQR + PSR

= 360 - 40 + 130 + 130

= 60  

Therefore, ∠SRQ = 60°