Question
Download Solution PDFIn the adjoining figure, PS is the bisector of ∠QPR and PT ⊥ QR and ∠Q > ∠R, then ∠TPS is -
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
PS is the bisector of angle QPR
PT is perpendicular to QR
Solution
In the ΔPQR,
∠RPS = ∠QPS = yº and ∠TPS = xº
In ΔPTR,
⇒ ∠(x + y)º + 90º + ∠R = 180 ..(1)
In ΔPTQ,
⇒ ∠(y - x)º + 90º + ∠Q = 180 ..(2)
Equating both equations,
⇒ ∠(x + y)º + 90º + ∠R = ∠(y - x)º + 90º + ∠Q
⇒ 2∠xº = ∠Q - ∠R
⇒ ∠xº = (∠Q - ∠R)/2
The correct option is 4.
Last updated on Jul 17, 2025
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