Geometry
Transversal Lines & Determining Angles
When a transversal crosses two parallel lines, it creates 8 angles. Alternate interior angles are equal, corresponding angles are equal, co-interior (same-side interior) angles are supplementary (add to 180°).
Watch & Learn
Watch a clear, friendly video explanation of Transversal Lines & Determining Angles:
Watch on YouTube →Opens a YouTube search for the best tutorial videos on this topic.
Worked Examples
Follow along with these step-by-step examples. Take your time — there's no rush!
Problem
A transversal crosses two parallel lines. One angle is 65°. Find the alternate interior angle.
Step-by-Step Solution
Alternate interior angles are equal when lines are parallel.
The alternate interior angle = 65°.
Answer
65°
Problem
A transversal creates an angle of 110°. Find the co-interior (same-side interior) angle.
Step-by-Step Solution
Co-interior angles are supplementary: they add to 180°.
180° − 110° = 70°
Answer
70°
Problem
Two parallel lines are cut by a transversal. One angle is 45°. Find the corresponding angle.
Step-by-Step Solution
Corresponding angles are equal (same position at each intersection).
Corresponding angle = 45°
Answer
45°
Problem
A transversal creates an angle of 130°. Find the supplementary angle on the same line.
Step-by-Step Solution
Supplementary angles add to 180°.
180° − 130° = 50°
Answer
50°
Problem
Two parallel lines are cut by a transversal. One angle is 75°. Find all 8 angles.
Step-by-Step Solution
The 4 angles at each intersection are: 75°, 105°, 75°, 105° (vertical and supplementary pairs).
Corresponding angles match across intersections.
All 8 angles: four 75° and four 105°.
Answer
Four angles of 75° and four angles of 105°
Your Turn — Practice Problems
Try all 5 problems on your own first. Write out your work — that's how it sticks!
💡 Tip: Don't peek at the answers until you've genuinely tried each one.
Alternate interior angle to 72°?
Co-interior angle to 85°?
Corresponding angle to 130°?
Vertically opposite angle to 55°?
Supplementary angle to 40°?
Alternate exterior angle to 60°?
Co-interior angle to 110°?
If one angle is 90°, what are all 8 angles when cut by a transversal?
Corresponding angle to 45°?
Supplementary angle to 75°?
Alternate interior angle to 115°?
If one angle is 50°, what is the vertically opposite angle?
Finished all 12? Give yourself a pat on the back — then check your work!
Keep going — you're on a roll!
Every topic you master is another step on your journey.
Explore More Topics