Question

if \\(\overline{uv} \cong \overline{ux}\\) and \\(m\angle uwx = 38^\circ\\), what is \\(m\angle vwx\\)?
\\(m\angle vwx = \square^\circ\\)

Explanation:

Step1: Use the Angle Bisector Theorem

Since \( \overline{UV}\cong\overline{UX}\), \(UW\) is the angle bisector of \( \angle V W X\) (by the converse of the angle bisector theorem: if a point is equidistant from the sides of an angle, then it lies on the bisector of the angle. Here \(U\) is equidistant from \(VX\) (as \( \overline{UV}\) and \( \overline{UX}\) are the distances from \(U\) to the sides of \( \angle V W X\))).
So \( \angle VWU=\angle XWU\).

Step2: Calculate \(m\angle VWX\)

We know that \(m\angle VWX = 2\times m\angle UWX\) (because \(UW\) bisects \( \angle VWX\)).
Given \(m\angle UWX = 38^{\circ}\), then \(m\angle VWX=2\times38^{\circ}\).

Answer:

\(76\)