Question

in the figure, \\( \triangle x y z \cong \triangle m n l \\).
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 \(\angle X=\angle M = 33^{\circ}\), \(\angle Z=\angle N=124^{\circ}\)

Step2: Apply the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). For \(\triangle XYZ\), we know that \(m\angle X + m\angle Y+m\angle Z=180^{\circ}\)

Step3: Substitute the known values

Substitute \(m\angle X = 33^{\circ}\) and \(m\angle Z = 124^{\circ}\) into the equation: \(33^{\circ}+m\angle Y + 124^{\circ}=180^{\circ}\)

Step4: Solve for \(m\angle Y\)

First, simplify the left - hand side: \(m\angle Y+157^{\circ}=180^{\circ}\). Then, subtract \(157^{\circ}\) from both sides: \(m\angle Y=180^{\circ}-157^{\circ}=23^{\circ}\)

Answer:

$23$