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

Explanation for the correct option:

Determine the type of triangle

In $∆\mathrm{ABC}$,
$\angle \mathrm{A}=\angle \mathrm{B}+\angle \mathrm{C}$
We know, sum of angles $=180$
$\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180$
$\angle \mathrm{A}+\angle \mathrm{A}=180$
$\angle \mathrm{A}=90°$
Thus, $∆\mathrm{ABC}$, is a right-angled triangle.

So, if one angle of a triangle is equal to the sum of the other two angles, then the triangle is a right triangle.

Hence, option (D) is the correct option.