Q

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

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.

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

In $\Delta$PRT, by using angle sum property
$\angle$PRT + $\angle$PTR + $\angle$TPR = $180^0$
So, $\angle$PTR  = $180^0 -95^0-40^0$
$\Rightarrow \angle PTR = 45^0$

Since lines, PQ and RS intersect at point T
therefore, $\angle$PTR = $\angle$QTS (Vertically opposite angles)
$\angle$QTS = $45^0$

Now, in $\Delta$QTS,
By using angle sum property
$\angle$TSQ + $\angle$STQ + $\angle$SQT = $180^0$
So, $\angle$SQT = $180^0-45^0-75^0$
$\therefore \angle SQT = 60^0$

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