Question

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

Answer 1

Answer:

Let us consider a triangle ABC whose angles are angle a, angle b and angle c.

As given, angle a = angle b + angle c....... (1)

By angle sum property of a triangle,

angle a + angle b + angle c= 180°

angle b + angle c + angle b + angle c = 180°

2 (angle b + angle c)=180°

angle b + angle c= 90°

i.e. angle a= 90°.......... [from (1)]