Question

Question 25

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

a) Obtuse
b) Acute
c) Right
d) Equilateral

Answer 1

Let A, B and C be the angles of the triangle. Then, one angle of a triangle is equal to the sum of the other two angles,
i.e. $\angle A=\angle B+\angle C$
As we know, $\angle A+\angle B+\angle C={180}^{\circ }$ [angle sum property of a triangle]
$\Rightarrow \angle A+\angle A={180}^{\circ }$ [from Eq. (i)]
$\Rightarrow 2\angle A={180}^{\circ }\Rightarrow \angle A=\frac{{180}^{\circ }}{2}\Rightarrow \angle A={90}^{\circ }$
Hence, the triangle is right angled.