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4. In Fig. 3.42, if lines PQ and RS intersect at point T, such that 4PRT0and < TSQ750, find 2 SQT. |
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Answer» Given: ∠PRT= 40°, ∠RPT=95°, ∠TSQ=75° In△PRT,∠PTR+∠PRT+∠RPT=180°[sum of interior angles of a triangle is180°].⇒∠PTR+40∘+95∘=180∘⇒∠PTR+135∘=180∘⇒∠PTR=180∘−135∘⇒∠PTR=45∘⇒∠QTR=∠PTR=45∘(vertically opposite angles) In△TSQ,∠QTS+∠TSQ+∠SQT=180∘[sum of interior angles of a triangle is180∘].45∘+75∘+∠SQT=180∘⇒120∘+∠SQT=180∘⇒∠SQT=180∘−120∘⇒∠SQT=60∘Hence, ∠SQT=60∘ hit like if you find it useful |
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