Question

ABC is a right angled triangle in which <A=90° and AB=AC.FIND <B and <C​

Answer 1

Given:

$AB = AC$

$\angle \: A = 90\degree$

$So ,\: \triangle \: ABC is \: \: a \: \: right-angled \: \: Isosceles$

$\therefore\angle B = \angle C$

( angles opposite to equal sides are equal )

We know that a Triangle measures 180°

By the question,

$\angle A + \angle B + \angle C = 180\degree$

( by angle sum property )

Let the unknown angles be x

$90\degree + x + x = 180\degree \\ \implies90 + 2x = 180 \\ \implies2x = 180 - 90 \\ \implies2x = 90 \\ \implies \: x = \dfrac{90}{2} \\ \implies \dfrac{ \cancel{90}}{{\cancel2}} \\ \implies \: x = 45\degree$

$\therefore \: x = 45\degree$

$So, \: \angle B \: \: and \: \angle C = 45 \degree$

$Now, \green{Verification}$

The angles are:-

$\angle B = 45 \degree$

$\angle C = 45 \degree$

$\angle A = 90 \degree$

We know that a triangle measures 180°

So,

$90\degree + 45 \degree + 45 \degree = 180\degree$

$90\degree + 90\degree = 180\degree$

$180\degree = 180\degree$

Hence, L.H.S = R.H.S

Proved