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

Solution:

It is given that

$\mathrm{AB}=\mathrm{AC}$

$\Rightarrow \angle C=\angle B$ (Angles opposite to equal sides are also equal)

$\ln \Delta \mathrm{ABC}$

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

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

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

$\Rightarrow 2 \angle B=90^{\circ}$

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

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