Question

In a triangle, one angle is greater than the sum of the other two angles. What type of triangle is this?

Answer 1

Given, one angle is greater than the sum of the other two angles

Let $\angle A,\angle Band\angle C$ be the interior angles of $△ABC$

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

Consider,

$$\begin{gathered} \angle A>\angle B+\angle C \\ \sin ce,\angle A+\angle B+\angle C=180° \\ \angle B+\angle C=180°-\angle A \end{gathered}$$

Then,

$$\begin{gathered} \angle A>180°-\angle A \\ \Rightarrow 2\angle A>180° \\ \Rightarrow \angle A>\frac{180°}{2} \\ \Rightarrow \angle A>90° \end{gathered}$$

So, $\angle A$ is an obtuse angle.

Hence, the triangle is an obtuse-angled triangle.