4. In Fig. 6.42, if lines PQ and RS intersect at point T, such that \angle PRT = 40°, \angle RPT = 95° and \angle TSQ = 75°, find \angle SQT.

                    

Answers (1)


We have,
lines PQ and RS intersect at point T, such that \angle PRT = 40°, \angle RPT = 95° and \angle TSQ = 75°

In \DeltaPRT, by using angle sum property
\anglePRT + \anglePTR + \angleTPR = 180^0
So, \anglePTR  = 180^0 -95^0-40^0
  \Rightarrow \angle PTR = 45^0

Since lines, PQ and RS intersect at point T
therefore, \anglePTR = \angleQTS (Vertically opposite angles)
                \angleQTS = 45^0

Now, in \DeltaQTS,
By using angle sum property
\angleTSQ + \angleSTQ + \angleSQT = 180^0
So, \angleSQT = 180^0-45^0-75^0
\therefore \angle SQT = 60^0

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