Question
Prove that if one angle of a triangle is equal to the sum of the other two angles, the triangle is right angled.
Solution
Let in ∆ABC,
∠A = ∠B + ∠C ...(1)
We know that,
∠A + ∠B + ∠C = 180°
| ∵ The sum of the three angles of a triangle is 180°
⇒ ∠A + ∠A = 180° | From (1)
⇒ 2 ∠A = 180°
Hence triangle ABC is right angled triangle.
