Question

$△\mathrm{ABC}$is an isosceles right-angled triangle in which $\angle A=90°$. Find $\angle B$ and $\angle C.$

Answer 1

Finding the valuer of $\angle B$ and $\angle C.$

Given

An isosceles right-angled triangle ,$\angle \mathrm{A}=90º$

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

We have learnt that angles opposite to equal sides are also equal

$\therefore \angle \mathrm{C}=\angle \mathrm{B}$

Let us assume $\angle \mathrm{B}=\angle \mathrm{C}=\mathrm{x}$

In $\mathrm{\Delta ABC},$

We have learnt that from angle sum property of triangle that the sum of interior angles of a triangle is $180°.$

$\begin{array}{rcl}\angle A+\angle B+\angle C& =& 180°\\ 90+x+x& =& 180\\ 90+2x& =& 180\\ 2x& =& 90\\ x& =& 45°\\ \therefore \angle B& =& \angle C=45°\end{array}$

Therefore the measure of angles are $\begin{array}{rcl}\angle B& =& \angle C=45°\end{array}$