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 equilateral triangle
• D. a right triangle

Answer 1

The correct option is D a right triangle

Sum of all angles of a triangle is ${180}^{\circ }$.

So, $\angle A+\angle B+\angle C={180}^{\circ }\dots \dots \left(1\right)$
As per question, $\angle A=\angle B+\angle C$
Let $\angle A=x$
Substitute in equation (1)
$x+x={180}^{\circ }$.
$2x={180}^{\circ }$
$x={90}^{\circ }$
$\angle B+\angle C={90}^{\circ }$