ABC is a right angled triangle in which \(\angle{A}\) = \(90^\circ\) and AB = AC, find \(\angle{B}\) and \(\angle{C}\).

In \(\triangle{ABC}\), we have,

AB = AC ...(Given)
\(\angle{B}\) = \(\angle{C}\) ...(i)(\(\because \) angles opposite to equal sides are equal)

Now, we know that,

\(\angle{A}\) + \(\angle{B}\) + \(\angle{C}\) = \(180^\circ\)
\(\Rightarrow \) \(90^\circ\) + \(\angle{B}\) + \(\angle{C}\) = \(180^\circ\) ...(given)
\(\Rightarrow \) \(90^\circ\) + \(\angle{B}\) + \(\angle{B}\) = \(180^\circ\) ...(from(i))
\(\Rightarrow \) 2 \(\angle{B}\) = \(180^\circ\) - \(90^\circ\)
\(\Rightarrow \) 2 \(\angle{B}\) = \(90^\circ\)
\(\Rightarrow \) \(\angle{B}\) = \(45^\circ\)
\(\therefore \) \(\angle{C}\) = \(45^\circ\), too.