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in \\( \triangle mno, \overline{m n} \cong \overline{o m} \\) and \\( m \angle m = 118 ^ { \circ } \\). find \\( m \angle o \\).
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Explanation:

Step1: Identify the triangle type

Since \(\overline{MN}\cong\overline{OM}\), \(\triangle MNO\) is an isosceles triangle. In an isosceles triangle, the base - angles are equal. Let \(\angle N=\angle O = x\).

Step2: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(\angle M+\angle N+\angle O = 180^{\circ}\). Substitute \(\angle M = 118^{\circ}\) and \(\angle N=\angle O=x\) into the equation: \(118^{\circ}+x + x=180^{\circ}\).

Step3: Solve the equation for \(x\)

Combine like terms: \(118^{\circ}+2x=180^{\circ}\). Subtract \(118^{\circ}\) from both sides: \(2x=180^{\circ}- 118^{\circ}=62^{\circ}\). Divide both sides by 2: \(x=\frac{62^{\circ}}{2}=31^{\circ}\).

Answer:

\(31^{\circ}\)