Question 8: In the given Figure, line AB || line CD and line PQ is the transversal. Ray PT and ray QT are bisectors of ∠BPQ and ∠PQD respectively. Prove that m ∠PTQ = 90 °.

Question 8: In the given Figure, line AB || line CD and line PQ is the transversal. Ray PT and ray QT are bisectors of BPQ and PQD respectively. Prove that m PTQ = 90 °.


Answer: 
AB || CD and PQ is a transversal line.
∠BPQ + ∠DQP = 180      (Angles on the same side of a transversal line are supplementary angles)

⇒ ∠QPT + ∠PQT = 90
In △PQT
∠QPT + ∠PQT + ∠PTQ = 180   (Angle sum property)
⇒ 90 + ∠PTQ = 180         
⇒ ∠PTQ = 90 
Hence proved.

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