Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer
which of the following statements about the image below is true?
line tx and line qs are perpendicular.
line ur and line qs are parallel.
the measure of ∠swx is 108°.
∠qrt and ∠tru are supplementary.

Explanation:

Step1: Check perpendicularity

For two lines to be perpendicular, the angle between them should be \(90^{\circ}\). There is no indication that line \(TX\) and line \(QS\) form a \(90^{\circ}\) angle.

Step2: Check parallelism

For two lines \(UR\) and \(QS\), there is no information (such as equal corresponding angles, alternate - interior angles etc.) to suggest they are parallel.

Step3: Check supplementary angles

\(\angle QRT = 18^{\circ}\) (vertically opposite to the given \(18^{\circ}\) angle). \(\angle TRU = 90^{\circ}\). \(18^{\circ}+90^{\circ}=108^{\circ}
eq180^{\circ}\), so they are not supplementary.

Step4: Calculate \(\angle SWX\)

We know that the sum of angles on a straight line is \(180^{\circ}\). Given \(\angle SWZ = 72^{\circ}\), then \(\angle SWX=180^{\circ}- 72^{\circ}=108^{\circ}\) (linear - pair of angles).

Answer:

The measure of \(\angle SWX\) is \(108^{\circ}\).