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Question
If an angle of a triangle is equal to the sum of the other two angles, find the type of the triangle
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Solution
Let ∠B is the greater angle than by the given condition ∠B = ∠A + ∠C.
Sum of three angles of a triangle = 180°
∠A + ∠B + ∠C = 180°
∠A + (∠A + ∠C) + ∠C = 180°
2∠A + 2∠C = 180°
2(∠A + ∠C) = 180°
∠A + ∠C = `(180^circ)/2`
∠B = 90°
∴ One of the angle of the triangle = 90°
It will be a right angled triangle.
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