Question

$ABC$ is a right angled triangle in which $\angle A={90}^{\circ }$ and $AB=AC$. Find $\angle B$ and $\angle C$.

Answer 1

Since $AB=AC,$

So, $△ABC$ is Right-angled isosceles.

$\angle B=\angle C$ ...(angles opp. to equal sides are equal)

$\angle A+\angle B+\angle C={180}^{\circ }$ ...(angle - sum property of a triangle)

Substituting $\angle B=\angle C,$ $\angle A={90}^o$

${90}^{\circ }+2\angle B={180}^{\circ }$

$2\angle B={180}^{\circ }–{90}^{\circ }={90}^{\circ }$

$\Rightarrow \angle B={45}^{\circ }$

So, $\angle C=\angle B={45}^o.$