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

One angle = sum of other two angles.

To prove:

It is right angled triangle.

Solution:

In $△ABC,$

$\angle A+\angle B=\angle C$ -----------(1)

We know

$\angle A+\angle B+\angle C={180}^o$ [sum of three angles of triangle is ${180}^o$]

$\angle C+\angle C={180}^o$ [from (1)]

$2\angle C={180}^o$

$\therefore \angle C={90}^o$

$\therefore △ABC$ is right angled triangle.