Question

If one angle of a triangle is equal to the sum of the two other angles, show that the triangle is right-angled.

Answer 1

Let ABC be a triangle and let $\angle A=\angle B+\angle C$.
Then,
$$\begin{gathered} \angle A+\angle B+\angle C=180°\left[\text{Sum of the angles of a triangle}\right] \\ \Rightarrow \angle A+\left(\angle B+\angle C\right)=180° \\ \Rightarrow \angle A+\angle A=180° \\ \Rightarrow 2\angle A=180° \\ \Rightarrow \angle A=90° \end{gathered}$$
Therefore, the triangle is right-angled at A.