# If one angle of a triangle is greater than the sum of the other two,

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.