Question

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Answer 1

Given, angle PRT=40°,angle RPT=95°and angle TSQ=75°

To find:-angle SQT

In triangle PRT,

By angle sum property of a triangle,
Angle PRT+ Angle RPT +angle PTR = 180°
»40°+95°+Angle PTR =180°
»135°+ Angle PTR =180°
»Angle PTR =180°-135°
»Angle PTR =55°

Now, since PQ and SR intersect each other,
Therefore,Angle PTR=Angle STQ =55°-(1)
(Vertically opposite angles)

Now in triangle SQT,
By angle sum property of a triangle,
Angle STQ+Angle SQT +angle TSQ=180°
»55°+angle SQT+75°=180° (from 1)
»130°+ANGLE SQT =180°
»Angle SQT =180°-130°
»Angle SQT =50°

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