which of the following statements about the image below is true? line ur and line vs are perpendicular. the measure of ∠swx is 72°. ∠swr and ∠wrs are supplementary. line ur and line vw are parallel.

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# Brief Explanations:
1. Analyze Option 1: Line $ UR $ and Line $ VS $ - From the diagram, $ UR $ and $ VS $ have right angles (perpendicular symbol), so they are perpendicular. Wait, no, let's check the angle at $ R $ and $ S $. Wait, the diagram shows a right angle at $ R $ for $ UR $ and another line, and at $ S $ for $ VS $ and another line. Wait, actually, let's check the angle between $ UR $ and $ VS $. Wait, maybe I misread. Wait, the angle between $ T $ and $ Q $ is $ 18^\circ $, and there's a right angle at $ R $ (so $ UR $ is perpendicular to some line, maybe the vertical line? Wait, no, let's check the other options.

2. Option 2: The measure of $ \angle SWX $ is $ 72^\circ $ - Wait, $ \angle WSR $ is $ 72^\circ $, but $ \angle SWX $: if $ VW $ and $ UR $ are related? Wait, no, maybe vertical angles or corresponding angles. Wait, no, let's check the third option.

3. Option 3: $ \angle SWR $ and $ \angle WRS $ are supplementary - Supplementary angles add to $ 180^\circ $. But $ \angle SWR $ and $ \angle WRS $: in triangle $ WRS $, the sum of angles is $ 180^\circ $, but they are two angles of a triangle, so they can't be supplementary (unless the third angle is $ 0^\circ $, which is impossible). So this is false.

4. Option 4: Line $ UR $ and Line $ VW $ are parallel - Wait, $ UR $ is perpendicular to some line, and $ VS $ is also perpendicular (right angle at $ S $). Wait, if $ UR \perp $ a transversal and $ VS \perp $ the same transversal, then $ UR \parallel VS $, but the option is $ UR \parallel VW $. Wait, maybe I made a mistake. Wait, let's re - examine the first option: "Line $ UR $ and Line $ VS $ are perpendicular". Wait, the diagram has a right angle at $ R $ (so $ UR $ is perpendicular to, say, $ RT $ or another line) and a right angle at $ S $ ( $ VS $ is perpendicular to $ WS $ or another line). Wait, no, the correct approach:

Wait, the angle between $ T $ and $ Q $ is $ 18^\circ $, and there's a right angle at $ R $, so the angle between $ UR $ and $ T $ is $ 90^\circ - 18^\circ=72^\circ $. Now, looking at the angle at $ S $, $ \angle WSR = 72^\circ $. If we consider the lines $ UR $ and $ VW $, the corresponding angles ( $ \angle $ between $ UR $ and transversal $ WR $, and $ \angle WSR $) are equal (both $ 72^\circ $), so by the corresponding angles postulate, $ UR \parallel VW $. Wait, but let's check the first option again. The first option says "Line $ UR $ and Line $ VS $ are perpendicular". But from the diagram, $ UR $ and $ VS $ have the same slope (if we consider the right angles), so they should be parallel, not perpendicular. So the fourth option "Line $ UR $ and Line $ VW $ are parallel" is correct? Wait, no, maybe I messed up. Wait, the right angle at $ R $ and $ S $: if $ UR \perp $ a line (say $ LR $) and $ VS \perp $ the same line $ LR $, then $ UR \parallel VS $. But the option is $ UR \parallel VW $. Wait, maybe the angle $ \angle WSR = 72^\circ $ and the angle between $ UR $ and $ WR $ is also $ 72^\circ $, so $ UR \parallel VW $ (corresponding angles). So the correct answer is "Line $ UR $ and Line $ VW $ are parallel" (the fourth option). Wait, but let's check the options again:

The options are:

1. Line $ UR $ and Line $ VS $ are perpendicular.

2. The measure of $ \angle SWX $ is $ 72^\circ $.

3. $ \angle SWR $ and $ \angle WRS $ are supplementary.

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

Let's analyze each:

- Option 1: If $ UR $ and $ VS $ are both perpendicular to the same line (e.g., the line through $ R $ and $ S $), then they should be parallel, not perpendicular. So this is false.

- Option 2: $ \angle SWX $: $ \angle WSR = 72^\circ $, and $ \angle SWX $ - if $ WX $ is a straight line with $ SW $, then $ \angle SWX $ would be supplementary to $ \angle WSR $ (if they are on a straight line), but $ \angle WSR = 72^\circ $, so $ \angle SWX = 180 - 72=108^\circ $, not $ 72^\circ $. So this is false.

- Option 3: $ \angle SWR $ and $ \angle WRS $: In triangle $ SWR $, the sum of angles is $ 180^\circ $. So $ \angle SWR+\angle WRS+\angle RSW = 180^\circ $. Since $ \angle RSW = 90^\circ $ (right angle at $ S $? Wait, no, the right angle is at $ S $ for $ VS $ and $ WS $? Wait, the diagram shows a right angle at $ S $, so $ \angle VSW = 90^\circ $, and $ \angle WSR = 72^\circ $, so $ \angle RSW = 90^\circ $? No, maybe the right angle is at $ R $ and $ S $ for different lines. Anyway, $ \angle SWR $ and $ \angle WRS $ are two angles of a triangle, so their sum is less than $ 180^\circ $ (since the third angle is positive), so they can't be supplementary. So this is false.

- Option 4: Line $ UR $ and Line $ VW $: The angle between $ UR $ and transversal $ WR $ is equal to the angle between $ VW $ and transversal $ WR $ (corresponding angles, both $ 72^\circ $), so by the corresponding angles postulate, $ UR \parallel VW $. So this is true.

# Answer:
Line $ UR $ and Line $ VW $ are parallel (the fourth option among the given options).

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