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Is one angle of a triangle is greater than the sum of the other two ,show that the triangle is obtuse angled?
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Is one angle of a triangle is greater than the sum of the other two ,s...
Let ∠A, ∠B and ∠C be the interior angles of ΔABC.

It is given that each angle is greater than the sum of the other two angles.

Consider ∠A > ∠B + ∠C

⇒ ∠A > 180deg – ∠A  [∠A + ∠B + ∠C = 180deg]

⇒ 2∠A > 180deg

⇒ ∠A > 90deg

Thus, ∠A is an obtuse angle.

Similarly, we will get ∠B is an obtuse angle and ∠C is an obtuse angle.

This means all the angles of ΔABC are obtuse, which is not possible.

So, the given condition should be: " One angle is greater than the sum of the other two angles".

Hence, ΔABC is an obtuse angled triangle.
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