Question

$△ABC$ is a right-angled triangle in which $\angle \mathrm{A}=90°$° and $\mathrm{AB}=\mathrm{AC}$. Find $\text{∠B}$ and $\angle C.$

Answer 1

Finding the $\text{∠B}$ and $\angle C$:

Given :

$\angle A=90°$ and

$\mathrm{AB}=\mathrm{AC}$
$\angle B=\angle C$ (Angles opposite to the equal sides)
We know that

$\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180°$ (Since the sum of the interior angles of the triangle equal to $180°$)
$\begin{array}{rcl}\angle A+\angle B+\angle B& =& 180°\\ 90°+2\angle B& =& 180°\\ 2\angle B& =& 180°-90°\\ \angle B& =& \frac{90°}{2}\\ \angle B& =& 45°\end{array}$

Therefore the value of $\angle B=\angle C=45°$