Question

if lines PQ and RS intersct at point T, such that angle PRT=40°, angle RPT= 95° and angle TSQ=75°, find angleSQT

Answer 1

from diagram we can write that STQ=PTR


in ∆PTR,

PTR+TPR+PRT=180

PTR=180-40-95=45°

so PTR=STQ=45

in ∆STQ

STQ+TSQ+TQS=180

SQT=180-45-75=60°

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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