Consider △PQR where PR is the longest sideSo we get PR>PQi.e. ∠Q>∠R..(1)We also know that PR>QRi.e. ∠Q>∠P..(2)By adding both the equations∠Q+∠Q>∠R+∠PSo we get2∠Q>∠R+∠PBy adding ∠Q on both LHS and RHS2∠Q+∠Q>∠R+∠P+∠QWe know that ∠R+∠P+∠Q=180∘So we get3∠Q>180∘By division∠Q>60∘So we get∠Q>32​(90∘)i.e. ∠Q>32​ of a right angleTherefore, it is proved that in a triangle, other than an equilateral triangle, angle opposite the longest side is greater 32​ of a right angle.