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

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

i.e. ∠B = ∠A + ∠C

Now, in ΔABC

Sum of all angles of triangle is 180°

∠A + ∠B + ∠C = 180°

∠B + ∠B = 180°[Therefore, ∠A + ∠C = ∠B]

2∠B = 180°

∠B = 90°

Therefore, ΔABC is right angled triangle.

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