Question

in a triangle Aba ,angle A=X ,angle B =3X,angle C=Y if 3Y-5X=30 prove that the triangle is right angle?

Answer 1

ΔABC
angel a =  x
angle b = 3x
angle c = y
3y - 5x = 30
3y = 30 + 5x
y = (30+5x)/3
angle c = (30+5x)/3
sum of all angles of triangle =180
x + 3x+(30+5x)/3=1+80
4x+(30/3)+(5x/3) =180
12x+30+5x=  180x3
                  = 540
17x +30 + 540
17x = 540-30
       = 510
x = 510/17
x=30
in a right angle triangle one of the angle is 90
x = 30
so 3x = 30x3
= 90
ΔABC is a right angle traingle