Question

question
in \\( \triangle l m n, \overline{l m} \cong \overline{n l} \\) and \\( m \angle l = 48 ^ { \circ } \\). find \\( m \angle n \\).

Explanation:

Step1: Identify the triangle type

Since \(\overline{LM}\cong\overline{NL}\), \(\triangle LMN\) is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal. So \(\angle M=\angle N\).

Step2: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle N = x\) and \(m\angle M=x\) (because \(\angle M\cong\angle N\)), and \(m\angle L = 48^{\circ}\). Then \(x + x+48^{\circ}=180^{\circ}\).
Simplify the equation: \(2x=180^{\circ}- 48^{\circ}\).
\(2x = 132^{\circ}\).
Solve for \(x\): \(x=\frac{132^{\circ}}{2}\).

Answer:

\(66^{\circ}\)