$ \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} $.

Academic Mathematics NCERT Class 9

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,

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

Simply Easy Learning

Updated on: 10-Oct-2022

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