Question 46·Easy·Lines, Angles, and Triangles
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 . What is the measure of angle at the intersection with the second track?
For parallel-lines angle questions, first mark the parallel lines and the transversal, then match the angle positions (corresponding, alternate interior, alternate exterior, or vertical). Once you identify the correct pair, use the equality (or supplementary) relationship to get the unknown angle quickly.
Hints
Identify the parallel lines and the transversal
The two railroad tracks are parallel, and the road is a transversal that intersects both of them.
Name the angle pair
Look at where the angle and angle sit between the two tracks. Are they on opposite sides of the road?
Apply the correct rule
If two angles are alternate interior angles formed by a transversal of parallel lines, they have the same measure.
Desmos Guide
No computation needed
This problem is based on a geometry rule for parallel lines, not arithmetic.
Use Desmos only as a check
If you want, you can type 52 in Desmos to keep the given angle visible while you compare it to angle in the diagram.
Step-by-step Explanation
Use the parallel-lines angle relationship
When a transversal crosses two parallel lines, alternate interior angles are equal.
In the figure, the angle and angle are alternate interior angles.
Conclude the measure of
Therefore, .
So, the measure of angle is .