Question

Prove that in a triangle other than an equilateral triangle, angle opposite the longest side is greater than 23 of a right angle.

Answer 1

Given -- ΔABC other than equilateral triangle.

The construction is already given in the picture.So let me just establish the relation between the sides.
Let AB = AD = DB

ABD is an equilateral triangle since AB = AD = DB

∠ABD = ∠ADB = ∠BAD = 60°

Longest side= BC
Angle opposite to longest side = ∠BAC

Here it is clear that ∠BAC = ∠BAD + ∠CAD
So ∠BAC > ∠BAD
∠BAC > 60°

Hence proved!

Hope This Helps You augusta
-navya