Question:
If one angle of a triangle is greater than the sum of the other two, show that the triangle is obtuse-angled.
Solution:
Let $\mathrm{ABC}$ be a triangle and let $\angle C>\angle A+\angle B$.
Then, we have:
$2 \angle C>\angle A+\angle B+\angle C \quad[$ Adding $\angle C$ to both sides $]$
$\Rightarrow 2 \angle C>180^{\circ}\left[\because \angle A+\angle B+\angle C=180^{\circ}\right]$
$\Rightarrow \angle C>\mathbf{9 0}^{\circ}$
Since one of the angles of the triangle is greater than $90^{\circ}$, the triangle is obtuse-angled.
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