Question 40·Easy·Lines, Angles, and Triangles
Two parallel hiking trails are shown on a map. A straight footpath crosses both trails, forming angles.
At the intersection with the first trail, the angle located between the two trails and to the right of the footpath measures . At the intersection with the second trail, the angle located between the two trails and to the right of the footpath is labeled .
What is the value of ?
For parallel lines cut by a transversal, first classify the given and unknown angles by position (between the lines or outside, same side or opposite side). Same-side interior angles are supplementary, so set their sum equal to and solve.
Hints
Identify the line relationship
The trails are parallel, and the footpath intersects both of them (it acts like a transversal).
Decide how the two marked angles are related
Both marked angles are between the parallel lines and on the same side of the transversal. What do those angles add to?
Write and solve an equation
Set up and solve for .
Desmos Guide
Compute the supplement
In Desmos, enter 180-65.
Read the result
The output is the value of .
Step-by-step Explanation
Use the relationship for parallel lines
The two trails are parallel and the footpath is a transversal. The two labeled angles lie between the parallel lines on the same side of the transversal, so they are supplementary:
Solve for
Subtract from both sides:
Therefore, .