Question

In fig., if lines PQ and RS intersect at point T, such that angle PRT =40degrees, angle RPT=95degrees and angle TSQ=75degrees, find angle SQT.

Answer 1

ang. ptr=180-(ang.prt+ ang. rpt)
=180-(40+95)
=180-135
=45

ang.ptr=ang.stq. ( vertically opposite angle)

ang sqt=180-(ang.stq+ang.tsq)
=180-(45+75)
=180-120
=60 (answer)

Answer 2

Hello mate ☺

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Solution:

In ∆PRT, we have

∠PRT+∠RPT+∠RTP=180°   (Sum of three angles of a triangle =180°)

⇒40°+95°+∠RTP=180°

⇒∠RTP=180°−40°−95°=45°

∠RTP=∠QTS     (Vertically Opposite Angles)

Therefore, ∠QTS is also equal to 45°

In ∆STQ, we have

∠SQT+∠TSQ+∠QTS=180°  (Sum of three angles of a triangle =180°)

⇒∠SQT+75°+45°=180°

⇒∠SQT=180°−75°−45°=60°

I hope, this will help you.☺

Thank you______❤

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