Question

if one angle of a triangle is equal to the sum of the other two show that the triangle is right angled

Answer 1

THE SUM OF THREE ANGLES IN A TRIANGLE 
A+B+C=180
HERE LET US CONSIDER A=B+C
THEN
B+C+B+C=180
2B+2C=180
B+C=90
SO ANGLE A SHOULD BE 90
SO IT IS A RIGHT ANGLED TRIANGLE

Answer 2

let A,B,C are the angles of triangle.
given A=B+C,
A+B+C=180 (angle sum property)
A+A=180 (given A=B+C)
2A=180
A=180/2
A=90.
( if one angle of a triangle is 90 it is an right angled triangle)
hence proved.