Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on yo
which of the following statements about the image below is true?
the measure of \\( \angle s w x \\) is \\( 72 ^ { \circ } \\).
\\( \angle s w r \\) and \\( \angle w r s \\) are supplementary.
line \\( u r \\) and line \\( v s \\) are perpendicular.
line \\( u r \\) and line \\( v w \\) are parallel.

Explanation:

Step1: Analyze the first option

$\angle SWX$ and the $72^{\circ}$ angle are not the same. $\angle SWX = 180^{\circ}- 72^{\circ}=108^{\circ}$ (linear - pair of angles). So the first option is wrong.

Step2: Analyze the second option

$\angle SWR = 72^{\circ}$ (given). $\angle WRS=180^{\circ}-(90^{\circ}+18^{\circ}) = 72^{\circ}$ (sum of angles in a triangle is $180^{\circ}$, right - angle is $90^{\circ}$). $72^{\circ}+72^{\circ}
eq180^{\circ}$, so they are not supplementary.

Step3: Analyze the third option

There is no indication that line $UR$ and line $VS$ are perpendicular.

Step4: Analyze the fourth option

Line $UR$ and line $VW$ are both perpendicular to the transversal (implied by the right - angles in the figure). If two lines are perpendicular to the same line, then they are parallel.

Answer:

Line $UR$ and Line $VW$ are parallel.