Question

question
in \\( \triangle w x y, \overline{w x} \cong \overline{y w} \\) and \\( m \angle w=64^{circ} \\). find \\( m \angle y \\).

Explanation:

Step1: Identify the triangle type

Since \(\overline{WX}\cong\overline{YW}\), \(\triangle WXY\) is an isosceles triangle. In an isosceles triangle, the base - angles are equal.

Step2: Apply the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle X = m\angle Y=x\). We know that \(m\angle W = 64^{\circ}\).
Using the formula \(m\angle W+m\angle X + m\angle Y=180^{\circ}\), substitute \(m\angle X=m\angle Y=x\) and \(m\angle W = 64^{\circ}\) into it:
\(64^{\circ}+x + x=180^{\circ}\)
\(64^{\circ}+2x=180^{\circ}\)

Step3: Solve for \(x\)

Subtract \(64^{\circ}\) from both sides of the equation \(64^{\circ}+2x=180^{\circ}\):
\(2x=180^{\circ}- 64^{\circ}\)
\(2x = 116^{\circ}\)
Divide both sides by \(2\): \(x=\frac{116^{\circ}}{2}=58^{\circ}\)

Answer:

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