Question

in the figure, \\( \triangle xyz \cong \triangle mnl \\).
find \\( m\angle y \\).
\\( m\angle y=\square^{\circ} \\)

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle XYZ\cong\triangle MNL\), corresponding angles are equal. So \(\angle X=\angle M\), \(\angle Y=\angle N\), \(\angle Z=\angle L\).

Step2: Calculate \(m\angle Y\)

We know that the sum of angles in a triangle is \(180^{\circ}\). But we can also use the fact that \(\angle Y\) and \(\angle N\) are supplementary to the angle adjacent (if we consider the property of congruent - triangle angle correspondence). Wait, no, more simply, since \(\triangle XYZ\cong\triangle MNL\), and in \(\triangle MNL\), we know one angle is \(124^{\circ}\) (let's assume \(\angle L = 124^{\circ}\)) and in \(\triangle XYZ\), \(\angle X=33^{\circ}\). Using the angle - sum property of a triangle (\(A + B + C=180^{\circ}\)). For \(\triangle XYZ\), \(m\angle X+m\angle Y+m\angle Z = 180^{\circ}\), and for \(\triangle MNL\), \(m\angle M+m\angle N+m\angle L=180^{\circ}\). Since \(\angle Z=\angle L\) (from congruence \(\triangle XYZ\cong\triangle MNL\)), we can also note that \(\angle Y\) and \(\angle N\) are related. But a better approach:
Since \(\triangle XYZ\cong\triangle MNL\), the angles of \(\triangle XYZ\) and \(\triangle MNL\) are equal. In \(\triangle MNL\), if we assume \(\angle L = 124^{\circ}\) (corresponding to \(\angle Z\)) and \(\angle M\) (corresponding to \(\angle X\)) is \(33^{\circ}\). Using the angle - sum formula for a triangle \(A + B + C=180^{\circ}\).
\(m\angle Y=180-(33 + 124)\)

$$m\angle Y=180 - 157$$

Answer:

\(23\)