Question

In ΔPQR, PQ = QR = RP = 7 cm, then find each angle of ΔPQR.
  

Answer 1

In ΔPQR, PQ = PR ...... (Given) 
 ... ∠Q = ∠R  (angles opposite to equal sides are equal) ... (i)
Again, QR = RP
∠Q = ∠P (angles opposite to equal sides are equal) ......  (ii)
From eqns (i) and (ii), we get 
∠P = ∠Q = ∠R
But in ΔPQR, we have 
  ∠P + ∠Q + ∠R = 180° 
 3 ∠P = 180°
⇒ ∠P = 60°
Hence, ∠P = ∠Q = ∠R = 60°

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