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Question

If one angle of a triangle is greater than the sum of other two so that the triangle is obtuse angle triangle

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Solution

=> Let ∠A, ∠B and ∠C be the interior angles of ΔABC.

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

Consider,
∠A > ∠B + ∠C

( ∠A + ∠B + ∠C = 180° )
(∠B + ∠C = 180 - ∠A )

then,
∠A > 180° – ∠A

2∠A > 180°

⇒ ∠A > 90°

Thus, ∠A is an obtuse angle.

Hence, ΔABC is an obtuse angled triangle


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