Question

The sum of two angles of a triangle is equal to its third angle . Determine he measure of the third angle .

Answer 1

In $\Delta ABC,$

Given that $\angle A+\angle C=\angle B$

But $\angle A+\angle B+\angle C={180}^{\circ }$ (Sum of angles of a triangle)
$\therefore \angle B+\angle A+\angle C={180}^{\circ }$
$\Rightarrow \angle B+\angle B={180}^{\circ }$ [Since, $\angle A+\angle C=\angle B$]
$\Rightarrow 2\angle B={180}^{\circ }$
$\Rightarrow \angle B=\frac{{180}^{\circ }}{2}={90}^{\circ }$
$\therefore$ Third angle =${90}^{\circ }$