Question

In the figure,if lines PQ and RS intersect at point T , Such that angle PRT = 40degree , angle RPT = 95degree , and angle TSQ = 75degree , find angle SQT​

Answer 1

Answer:

In PRT

By angle sum property of triangle

∠PRT+∠RPT+∠PTR=180

∘

⇒90

∘

+45

∘

+∠PTR=180

∘

⇒135

∘

+∠PTR=180

∘

⇒∠PTR=180

∘

−135

∘

⇒∠PTR=45

∘

.

Also,

∠STQ=∠PTR

∠STQ=45

∘

(vertically opposite angles)

In ΔSQT

By angle sum property of triangle

∠SQT+∠STQ+∠TSQ=180

∘

∠SQT+75

∘

+45

∘

=180

∘

∠SQT+120

∘

=180

∘

∠SQT=180

∘

−120

∘

∠SQT=60

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