Question

In Fig., PQ⊥PS, PQ||SR, ∠SQR = 28⊥ and ∠QRT = 65°. then find the value of x and y.

Answer 1

PQ⊥PS, PQ⊥SR,

∠SQR = 28, ∠QRT = 65,

Then x = ? y = ?

∠QRT + ∠QRS = 180° (∵ Linear pairs)

65 + ∠QRS = 180

∠QRS = 180 – 65

∴∠QRS =115°

In ∆SRQ,

∠QRS + ∠SQR + ∠RSQ = 180°

115 + 28 + ∠RSQ = 180

∴∠RSQ =180 – 143

∴∠RSQ = 37

Now, ∠RSQ = ∠PQS 37° = x

∴x = 37

In ∆SPQ,

∠SPQ + ∠PSQ + ∠PQS = 180°

90 + y + 37 = 180

∴y = 180- 127

∴y = 53°.