Question

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

Answer 1

Given:
∠A = ∠B + ∠C
​We know:
∠A + ∠B + ∠C = 180^o
⇒ ∠B +∠C + ∠B + ∠C = 180^o
​ ⇒ 2∠B + 2∠C = 180^o
​ ⇒ 2(∠B +∠C) = 180^o
​ ⇒ ∠B + ∠C = 180/2
⇒ ​∠B + ∠C = 90^o
$\therefore$ ∠A = 90^o
This shows that the triangle is a right angled triangle.