Question

in \\( \triangle vwx \\), \\( \overline { vw } \cong \overline { xv } \\) and \\( m \angle v = 47 ^ { \circ } \\). find \\( m \angle x \\).

Explanation:

Step1: Identify the triangle type

Since \(\overline{VW}\cong\overline{XV}\), \(\triangle VWX\) is an isosceles triangle. In an isosceles triangle, the base - angles are equal.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle W = m\angle X=x\). Then \(m\angle V + m\angle W+m\angle X = 180^{\circ}\).
Substitute \(m\angle V = 47^{\circ}\) and \(m\angle W = m\angle X=x\) into the equation: \(47^{\circ}+x + x=180^{\circ}\).

Step3: Solve the equation for \(x\)

Combine like terms: \(47^{\circ}+2x = 180^{\circ}\).
Subtract \(47^{\circ}\) from both sides: \(2x=180^{\circ}- 47^{\circ}=133^{\circ}\).
Divide both sides by \(2\): \(x=\frac{133^{\circ}}{2}=66.5^{\circ}\).

Answer:

\(66.5^{\circ}\)