Question

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

Answer 1

In the triangle ABC,

$\angle B=\angle A+\angle C$
$\text{B}ut\angle A+\angle B+\angle C={180}^{\circ }$
$\Rightarrow \angle B+\angle A+\angle C={180}^{\circ }$
$\Rightarrow \angle B+\angle B={180}^{\circ }\Rightarrow 2\angle B={180}^{\circ }$
$\therefore \angle B=\frac{{180}^{\circ }}{2}={90}^{\circ }$
$\because$ One angle of triangle is ${90}^{\circ }$
$\therefore \Delta ABC$ is a right triagle.