Question

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

Answer 1

Finding the $\angle B$ and $\angle C$.:

Solution:

In $△\mathrm{ABC}$

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

Therefore, $\Delta ABC$ is a right-angled isosceles

$\angle B=\angle C$ (angles opposite to equal sides are equal)

$\angle A+\angle B+\angle C=180°$ (angle-sum property of a triangle)

Substituting$\angle B=\angle C,\angle A=90°$

$90°+2\angle B=180°$

$\begin{array}{rcl}2\angle B& =& 180°-90°\\ 2\angle B& =& 90°\\ \angle B& =& 45°\end{array}$

$\angle B=\angle C=45°$

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