Question

look at this diagram:
if \\( \overleftrightarrow { r t } \\) and \\( \overleftrightarrow { u w } \\) are parallel lines and \\( m \angle r s v = 70 ^ { \circ } \\), what is \\( m \angle w v s \\)?
work it out
not feeling ready yet? these can help:

Explanation:

Step1: Use the property of consecutive interior angles

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. Here, \(\overleftrightarrow{RT}\) and \(\overleftrightarrow{UW}\) are parallel lines and \(XQ\) is the transversal. \(\angle RSV\) and \(\angle WVS\) are consecutive interior angles.

Step2: Apply the supplementary - angle formula

If two angles \(\alpha\) and \(\beta\) are supplementary, then \(\alpha+\beta = 180^{\circ}\). Let \(\alpha=\angle RSV = 70^{\circ}\) and \(\beta=\angle WVS\). So, \(m\angle RSV+m\angle WVS=180^{\circ}\).
Substitute \(m\angle RSV = 70^{\circ}\) into the equation: \(70^{\circ}+m\angle WVS=180^{\circ}\).
Solve for \(m\angle WVS\): \(m\angle WVS=180^{\circ}- 70^{\circ}\).

Answer:

\(110\)