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ABC is a right angled triangle in which ∠ A = 90° and AB = AC. Find ∠ B and ∠ C.

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

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In the triangle ABC, sides AB and AC are equal.

We know that angles opposite to equal sides are also equal.

Thus,            $\angle B\ =\ \angle C$

Also, the sum of the interior angles of a triangle is $180^{\circ}$.

So, we have :

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

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

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

Hence                        $\angle B\ =\ \angle C\ =\ 45^{\circ}$

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