Question

Question 2
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 answer is D.
Let the angles of a $\Delta ABC$ be $\angle A,\angle Band\angle C$
Given, $\angle A=\angle B+\angle C$ . . . . .(i)
In $\Delta ABC,\angle A+\angle B+\angle C=180$ [sum of all the angles of a triangle is ${180}^{\circ }$] . . . . .(ii)
From Eqs. (i) and (ii),
$\angle A+\angle A={180}^{\circ }$
$\Rightarrow 2\angle A={180}^{\circ }$
$\Rightarrow \angle A=\frac{{180}^{\circ }}{2}$
$\therefore \angle A={90}^{\circ }$
Hence, the triangle is a right triangle.