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

Let the first angle be a and second angle be b

According to question,

Third angle = a + b

Now,

By angle sum property of triangle,

First angle + second angle + third angle = 180

=> a + b + a +b = 180

=> 2a + 2b = 180

=> a + b = 90°

=> Third angle = 90°

So, the given triangle is right angled.

Answer 2

Let two angles are ( x and y )

Third Angie = ( x + y )



We know,
Sum of all Angles of at vertices of a triangle is 180



Here,

x + y + x + y = 180

2(x + y ) =180

x + y = 90






x + y = third angle = 90

Hence, one angle is of 90°




$\fcolorbox{yellow}{blue}{proved}$