Q9 of 53 Page 158

In ΔPQR, if m∠P + m∠Q = m∠R. PR = 7, QR = 24, then PQ =


In ΔABC, we know that sum of all interior angles in triangle is equal to 180°


⇒ ∠P + ∠Q + ∠R = 180


Also, given that, ∠P + ∠Q = ∠R,


⇒ 2∠R = 180


⇒ ∠R = 90°


Using Pythagoras Theorem,


PQ2 = PR2 + QR2


⇒ PQ2 = 72 + (24)2


⇒ PQ2 = 49 + 576


⇒ PQ2 = 625


⇒ PQ = 25


∴ Option (b) is correct.

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