Class 9 Exam > Class 9 Questions > PQRS is a square and SRT is an equilateral tr...
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PQRS is a square and SRT is an equilateral triangle. The measure of ∠TQR is:
- a)25°
- b)55°
- c)15°
- d)35°
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
PQRS is a square and SRT is an equilateral triangle. The measure of &a...
In ΔS PTS and QTR
(TR = TS = SR = PQ = QR = PS)
TR = TR (given)
PS = QR (given)
∠PST = ∠QRT
= 90° + 60° = 150°
(Square) (equilateral Δ)
∴ ΔPTS = ΔQTR
(By R-H-S congruence criterion)
TP = TQ (C.P.C.T)
∴ ∠TPS = ∠TQR (C.P.C.T)
Now,
In ΔTQR
TR = RQ
∴ ∠RTQ = ∠RQT, and
∠RTQ + ∠RQT +∠R = 180°
⇒ 2∠RQT + 90° + 60° = 180°
(TR = TS = SR = PQ = QR = PS)
TR = TR (given)
PS = QR (given)
∠PST = ∠QRT
= 90° + 60° = 150°
(Square) (equilateral Δ)
∴ ΔPTS = ΔQTR
(By R-H-S congruence criterion)
TP = TQ (C.P.C.T)
∴ ∠TPS = ∠TQR (C.P.C.T)
Now,
In ΔTQR
TR = RQ
∴ ∠RTQ = ∠RQT, and
∠RTQ + ∠RQT +∠R = 180°
⇒ 2∠RQT + 90° + 60° = 180°
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PQRS is a square and SRT is an equilateral triangle. The measure of ∠TQR is:a)25°b)55°c)15°d)35°Correct answer is option 'C'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about PQRS is a square and SRT is an equilateral triangle. The measure of ∠TQR is:a)25°b)55°c)15°d)35°Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for PQRS is a square and SRT is an equilateral triangle. The measure of ∠TQR is:a)25°b)55°c)15°d)35°Correct answer is option 'C'. Can you explain this answer?.
PQRS is a square and SRT is an equilateral triangle. The measure of ∠TQR is:a)25°b)55°c)15°d)35°Correct answer is option 'C'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about PQRS is a square and SRT is an equilateral triangle. The measure of ∠TQR is:a)25°b)55°c)15°d)35°Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for PQRS is a square and SRT is an equilateral triangle. The measure of ∠TQR is:a)25°b)55°c)15°d)35°Correct answer is option 'C'. Can you explain this answer?.
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