Question

look at this diagram:
if \\( \overleftrightarrow { rt } \\) and \\( \overleftrightarrow { uw } \\) are parallel lines and \\( m \angle w x = 139 ^ { circ } \\), what is \\( m \angle u v x \\)?
submit

Explanation:

Step1: Identify supplementary angles

Since \( \overleftrightarrow{RT} \parallel \overleftrightarrow{UW} \) and \( \overleftrightarrow{XQ} \) is a transversal, \( \angle WVX \) and \( \angle UVX \) are supplementary? Wait, no, actually \( \angle WX V \) (wait, the angle given is \( \angle WX V \)? Wait, the problem says \( m\angle WX V = 139^\circ \), and we need \( m\angle UVX \). Wait, actually, since \( RT \parallel UW \), and the transversal is \( XQ \), then \( \angle UVX \) and \( \angle WXV \) are same - side interior angles? Wait, no, let's correct. Wait, \( \angle WXV \) and \( \angle UVX \): since \( RT \parallel UW \), and the transversal is \( XQ \), then \( \angle UVX \) and \( \angle WXV \) are same - side interior angles? Wait, no, actually, \( \angle WXV \) and \( \angle UVX \) are supplementary? Wait, no, let's think again. Wait, \( \angle WXV = 139^\circ \), and we need \( \angle UVX \). Since \( RT \parallel UW \), the consecutive interior angles are supplementary. Wait, \( \angle UVX \) and \( \angle WXV \): wait, no, maybe \( \angle UVX \) and \( \angle WXV \) are same - side interior angles, so they should be supplementary? Wait, no, let's check the diagram. The lines \( RT \) and \( UW \) are parallel, and the transversal is \( XQ \). So \( \angle UVX \) and \( \angle WXV \): if we consider the parallel lines \( RT \) and \( UW \), and transversal \( XQ \), then \( \angle UVX \) and \( \angle WXV \) are same - side interior angles, so they are supplementary. Wait, but actually, \( \angle UVX + \angle WXV = 180^\circ \)? Wait, no, maybe I got the angles wrong. Wait, the angle given is \( \angle WX V = 139^\circ \), and we need \( \angle UVX \). Wait, actually, \( \angle UVX \) and \( \angle WXV \) are supplementary because they are same - side interior angles formed by parallel lines and a transversal. So:
\( m\angle UVX + m\angle WXV=180^\circ \)

Step2: Solve for \( m\angle UVX \)

We know that \( m\angle WXV = 139^\circ \), so substitute into the equation:
\( m\angle UVX=180^\circ - 139^\circ \)
\( m\angle UVX = 41^\circ \)

Answer:

\( 41 \)