Question

Prove that if one angle of a triangle is equal to the sum of the other two angles, then the triangle is right angled.

Answer 1

Let the angles be x, y, z.

Given,
x = y + z

We know that,
Sum of angles in a triangle is 180°

So,

x + ( y + z) = 180

x + x = 180

2x = 180

x = 90

Therefore, The triangle is right angled as one of the angle is 90°

Hope helped!

Answer 2

let 3 angles be a,b,c

As we know in triangle

a+ b+c = 180

And it's given that a= b+ c

Substitute a= b+c in a + b+c = 180

b+c +b +c = 180

2(b+c)= 180

b+c = 90

As a= b+c

So a= 90

As we know if one angle is 90

then it's right angled triangle

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