Question

In a triangle ABC, one of the angles is 50% more than the sum of the other two angles. Find the largest angle.

Answer 1

Let largest angle of the triangle be c
Sum of other two angles of the triangle be x
Given c=1.5*x
and we know c= 180-x
So 1.5x=180-x
2.5x=180
x=180/2.5=72
c=1.5x=1.5*72=108
So the largest angle of the triangle is 108°

Answer 2

it is given that ABC is a triangle in which one of angles is 50 % more than the sum of the other two angles.

let A = (B + C) + 50% of (B + C)

⇒A = (B + C) + 50 × (B + C)/100

⇒A = (B + C) + (B + C)/2

⇒A = 3/2 (B + C)........(1)

we know sum of all angles of triangle is 180°

⇒ A + B + C = 180°

from equation (1) we get,

⇒3(B + C)/2 + (B + C) = 180°

⇒5(B + C)/2 = 180°

⇒(B + C) = 360/5 = 72°

so ∠ A = 180° - (B + C) = 180° - 72° = 108°

therefore largest angle, ∠A = 108°