O is the incentre of the ΔPQR. If ∠POR = 120 degree, then what is the ΔPOR ?

45 degree 60 degree 55 degree 48 degree

60 degree

We know that,  Angle at incentre = 90° + \(\frac{ vertex \; angle }{2}\) = ∠POR = 120°  = ∠POR = 90°  + \(\frac{ ∠PQR }{2}\) = 120° = 90 + \(\frac{ ∠PQR }{2}\) = \(\frac{ ∠PQR }{2}\) = 120 - 90 = ∠PQR = 30° × 2 = 60°