Question

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

• A. isosceles
• B. equilateral
• C. right angled
• D. ordinary

Answer 1

The correct option is C right angled

Let's consider a triangle ABC, in which angle A equals the sum of other two angles.
$\angle A=\angle B+\angle C$....................................(1)

Since the sum of three angles of a triangle is ${180}^0$
$\angle A+\angle B+\angle C={180}^0$

From (1) we have,
$\angle A+\angle A={180}^0$
$2\angle A={180}^0$
$\angle A={90}^0$

This gives
$\angle B+\angle C={90}^0$

So the triangle is Right angled as one of the angle is 90 degree.