Alternate Angles
Worked Example
Problem: A transversal crosses two parallel lines. One of the alternate interior angles measures 65°. What is the measure of the other alternate interior angle?
Step 1: Identify the angle pair. The two angles are on opposite sides of the transversal and both lie between the parallel lines, so they are alternate interior angles.
Step 2: Apply the alternate angles theorem: when lines are parallel, alternate interior angles are equal.
Alternate angle=65°
Answer: The other alternate interior angle also measures 65°.
Why It Matters
Alternate angles give you a direct way to find unknown angles whenever a transversal cuts through parallel lines. They are also used as a key step in proving that two lines are parallel — if a pair of alternate angles is equal, the lines must be parallel. This reasoning appears throughout geometry proofs and real-world problems involving parallel structures.
Common Mistakes
Mistake: Confusing alternate angles with co-interior (same-side interior) angles.
Correction: Alternate angles are on opposite sides of the transversal and are equal when lines are parallel. Co-interior angles are on the same side and are supplementary (sum to 180°).
Related Terms
- Alternate Interior Angles — Alternate angles located between the two lines
- Alternate Exterior Angles — Alternate angles located outside the two lines
- Transversal — The line that crosses two others to form these angles
- Parallel Lines — Lines for which alternate angles are equal
- Corresponding Angles — Another equal-angle pair formed by a transversal