if the bisector of the base angles of traingle enclose an angle 135 Deg. , prove that the triangle is a right angle traingle.

Hello student,
Please find the answer to your question below
let inΔABC∠A=90
In ΔABC, BP and CP are bisectors of angles B and C respectively.
Hence ∠A + ∠B + ∠C = 180°
∠A + 2∠1 + 2∠2 = 180°
2(∠1 + ∠2) = 180° – ∠A
(∠1 + ∠2) = 90° – (∠A/2) --- (1)
In ΔPBC, ∠P + ∠1 + ∠2 = 180°
∠P + [90° – (∠A/2)] = 180° [From (1)]
∠P = 180° – [90° – (∠A/2)]
= [90° + (∠A/2)]
∠P=90°+(90/2)°
∠P=135°
So it is shown that ifΔABC is a right angled triangle its bisectors enclose a angle of 135°