Question 384·Easy·Math

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A service road crosses two parallel railroad tracks, as shown in the figure.

At the intersection with the first track, the acute angle between the road and the track measures $52^\circ$ . What is the measure of angle $x$ at the intersection with the second track?

A road cutting across parallel tracks is a transversal. Look for labeled angles between the tracks on opposite sides of the road. They form alternate interior angles: angles between parallel lines on opposite sides of a transversal are equal. Check their positions before subtracting from $180^\circ$ ; that subtraction finds a neighboring angle, not its match.

Hints

Hint 1
Look between the tracks. Angles in that space are interior angles. The two labeled angles sit on opposite sides of the road. What kind of pair does that make them?
Hint 2
The road is a transversal, a line crossing both tracks. Across parallel tracks, alternate interior angles have equal measures. How does that connect $x$ to the marked angle?

Step-by-step

Match alternate interior angles
Step 1
Identify the equal-angle pair
No Desmos needed. A parallel-line angle fact gives the measure directly. Both labeled angles lie between the tracks: one is below Track 1, and the other is above Track 2. They’re on opposite sides of the road, so they’re alternate interior angles. Because the tracks are parallel, their measures are equal:
$x^\circ=\text{measure of the angle below Track 1, left of Road}.$
Step 2
Use the marked measure
The angle below Track 1 is marked $52^\circ$ , so put that given measure into the equality:
$x^\circ=52^\circ.$
The angle at Track 2 measures $52^\circ$ . Choice A.

Lessons that teach this

SAT Geometry and TrigonometryBeginnerCoreUse line and angle relationships

Question 384·Easy·Math

Strategy

Hints

Step-by-step

Lessons that teach this

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Strategy

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Step-by-step

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