Question

If one angle of a triangle is greater than the sum of the other two angles, then what can you say about the measure of this angle? What type of a triangle is this?

Answer 1

Let's take $\text{△ABC,}$

According to the question, one angle of the triangle is greater than the sum of two angle of the triangle.

Therefore, $\angle A>\angle B+\angle C------------\left(i\right)$

Now, $\text{∠A+∠B+∠C = 180° (Angle sum porperty of triangle)}$

$$\begin{gathered} \text{∠A+∠A > 180° ---------(from eq. (i))} \\ \text{2∠A > 180°} \\ \text{∠A > 180÷2} \\ \text{∠A > 90°} \end{gathered}$$

Hence, the value of that angle will be greater than $90°.$

Since, one angle of a triangle is greater than $90°$,

Therefore, the given triangle is an obtuse-angled triangle.