Question

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is:

• A. an isosceles triangle
• B. an obtuse triangle
• C. an equilteral triangle
• D. a right triangle

Answer 1

The correct option is D

a right triangle

Let $\angle A,\angle B,\angle C$ be the angles of a $\Delta ABC$ and let $\angle A=\angle B+\angle C$

But $\angle A+\angle B+\angle C={180}^{\circ }$ (Sum of angles of a triangle)

$\therefore \angle A+\angle A={180}^{\circ }\Rightarrow 2\angle A={180}^{\circ }$

$\Rightarrow \angle A=\frac{{180}^{\circ }}{2}={90}^{\circ }$

$\therefore \Delta$ is a right angled triangle.