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Question -

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



Answer -

In the triangle ABC,
 
∠B = ∠A + ∠C
But ∠A + ∠B + ∠C = 180°
⇒∠B + ∠A + ∠C = 180°
⇒∠B + ∠B = 180°
⇒2∠B = 180°
∴ ∠B =  = 90°
∵ One angle of the triangle is 90°
∴ ∆ABC is a right triangle.

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