(ii) Find TSQ R 80° T 40° Р S Q tell in short answer
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Class 11
>>Applied Mathematics
>>Straight lines
>>General equation of a line
>>In fig, if lines PQ and RS intersect at
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In fig, if lines PQ and RS intersect at a point T such that ∠PRT=40
∘
,∠RPT=95
∘
and ∠TSQ=75
∘
, find ∠SQT.
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Solution
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In PRT
By angle sum property of triangle
∠PRT+∠RPT+∠PTR=180
∘
⇒90
∘
+45
∘
+∠PTR=180
∘
⇒135
∘
+∠PTR=180
∘
⇒∠PTR=180
∘
−135
∘
⇒∠PTR=45
∘
.
Also,
∠STQ=∠PTR
∠STQ=45
∘
(vertically opposite angles)
In ΔSQT
By angle sum property of triangle
∠SQT+∠STQ+∠TSQ=180
∘
∠SQT+75
∘
+45
∘
=180
∘
∠SQT+120
∘
=180
∘
∠SQT=180
∘
−120
∘
∠Sqt=6
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