Question

The angles of a triangle are in the ratio 2:1:3. Show that the triangle is a right angled triangle.

Answer 1

angles are in the ratio of 2:1:3 ,so angles will be 2x:x:3x, &on sum of right angle triangle is always 180 degree 
2x+x+3x=180
6x=180
x=30 degree
2x=2*30=60 degree
3x=90 degree
when an angle of triangle becomes 90 degree it becomes right angle triangle.

Answer 2

w.k.t the sum of the angles of a triangle=180
let the angles of a triangle be 2x, x,3x
so  2x+x+3x=180
6x=180
x=180/6=30x=30
2x=60
3x=90
since in a triangle one angle is 90 it is a right angle triangle