If one angle of a triangle is equal to the sum of the other two, show that the triangle is a right triangle.

Question

Philoid · Accepted Answer

If one of the angle of a triangle is equal to the sum of other two.

i.e. ∠B = ∠A + ∠C

Now, in

Sum of all angles of triangle is 180^o

∠A + ∠B + ∠C = 180^o

∠B + ∠B = 180^o [Therefore, ∠A + ∠C = ∠B]

2∠B = 180^o

∠B = 90^o

Therefore, ABC is right angled triangle.