Question

question
in \\( \triangle w x y, \overline{x y} \cong \overline{w x} \\) and \\( \mathrm{m} \angle w=61^{\circ} \\). find \\( \mathrm{m} \angle x \\).

Explanation:

Step1: Identify the triangle type

Since \(\overline{XY}\cong\overline{WX}\), \(\triangle WXY\) is an isosceles triangle. In an isosceles triangle, the base - angles are equal. So, \(\angle Y=\angle W = 61^{\circ}\).

Step2: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle X=x\). Then, by the triangle - angle sum theorem \(m\angle W + m\angle X+m\angle Y=180^{\circ}\).
Substitute \(m\angle W = 61^{\circ}\) and \(m\angle Y = 61^{\circ}\) into the equation: \(61^{\circ}+x + 61^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

Combine like terms: \(x+122^{\circ}=180^{\circ}\).
Subtract \(122^{\circ}\) from both sides: \(x=180^{\circ}- 122^{\circ}\).
\(x = 58^{\circ}\).

Answer:

\(m\angle X = 58^{\circ}\)