# If one angle of a triangle is equal to the sum of the other two, show that the triangle is right-angled.

Question:

If one angle of a triangle is equal to the sum of the other two, show that the triangle is right-angled.

Solution:

Let ABC be a triangle.

Then, $\angle A=\angle B+\angle C$

$\therefore \angle A+\angle B+\angle C=180^{\circ} \quad$ [Sum of the angles of a triangle]

$\Rightarrow \angle B+\angle C+\angle B+\angle C=180^{\circ}$

$\Rightarrow 2 \angle B+\angle C=180^{\circ}$

$\Rightarrow \angle B+\angle C=90^{\circ}$

$\Rightarrow \angle A=\mathbf{9 0}^{\circ} \quad[\because \angle A=\angle B+\angle C]$

This implies that the triangle is right-angled at A.