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In Δ PQR, PS is the bisector of ∠ P and PT ⊥ OR, then ∠ TPS is equal to:
  • a)
    ∠Q + ∠ R
  • b)
    900 + 1/2 ∠Q
  • c)
    900 - 1/2 ∠R
  • d)
    1/2 (∠ Q - ∠ R)
  • e)
    None of These
Correct answer is option 'D'. Can you explain this answer?

Answers

∠1 + ∠2 = ∠3 [PS is bisector.] ------ (1)
∠Q = 900 - ∠1
∠R = 900 -∠2 - ∠3
So,
∠Q - ∠R = (900 - ∠1) - (900 - ∠2 - ∠3)
∠Q - ∠R = ∠2 + ∠3 - ∠1
∠Q - ∠ R = ∠2 + (∠1 + ∠2) -∠1[using equation 1]
∠Q - ∠R = 2 ∠2
1/2 * (∠Q - ∠R) = ∠TPS.

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In Δ PQR, PS is the bisector of ∠P and PT ⊥ OR, then ∠TPS is equal to:a)∠Q + ∠ Rb)900+ 1/2 ∠Qc)900- 1/2 ∠Rd)1/2 (∠ Q - ∠ R)e)None of TheseCorrect answer is option 'D'. Can you explain this answer? for GMAT 2023 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In Δ PQR, PS is the bisector of ∠P and PT ⊥ OR, then ∠TPS is equal to:a)∠Q + ∠ Rb)900+ 1/2 ∠Qc)900- 1/2 ∠Rd)1/2 (∠ Q - ∠ R)e)None of TheseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2023 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In Δ PQR, PS is the bisector of ∠P and PT ⊥ OR, then ∠TPS is equal to:a)∠Q + ∠ Rb)900+ 1/2 ∠Qc)900- 1/2 ∠Rd)1/2 (∠ Q - ∠ R)e)None of TheseCorrect answer is option 'D'. Can you explain this answer?.
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∠1 + ∠2 = ∠3[PS is bisector.] ------ (1)∠Q = 900- ∠1∠R = 900-∠2 - ∠3So,∠Q - ∠R = (900- ∠1) - (900- ∠2 - ∠3)∠Q - ∠R = ∠2 + ∠3 - ∠1∠Q - ∠ R = ∠2 + (∠1 + ∠2) -∠1[using equation 1]∠Q - ∠R = 2 ∠21/2 * (∠Q - ∠R) = ∠TPS.