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

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Given:

$ABC$ is a right-angled triangle in which $\angle A=90^o$ and  $AB=AC$.

To do:

We have to find $\angle B$ and $\angle C$.

Solution:

Given, that $AB=AC$

We know that,

The angles opposite to the equal sides are also equal.

This implies,

$\angle B = \angle C$

We know that,

The sum of the interior angles of a triangle is always equal to $180^o$

This implies

In $\triangle ABC,$

$\angle A+\angle B+\angle C = 180^o$

Therefore,

$90^o+2\angle B=180^o$  (since $\angle B = \angle C$)

This implies,

$2\angle B=90^o$

$\angle B=\frac{90^o}{2}$

$\angle B=45^o$

Therefore,

$\angle B=\angle C=45^o$.

Updated on 10-Oct-2022 13:41:12