Transversal Angles Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
A transversal crosses two parallel lines. One of the angles formed is 65°65°. Find the corresponding angle and the alternate interior angle.

Solution

  1. 1
    Step 1: Corresponding angles are in the same position at each intersection (both above-left, or both below-right, etc.). When lines are parallel, corresponding angles are equal. So the corresponding angle is also 65°65°.
  2. 2
    Step 2: Alternate interior angles are between the parallel lines, on opposite sides of the transversal. When lines are parallel, alternate interior angles are equal. So the alternate interior angle is also 65°65°.
  3. 3
    Step 3: Summary: corresponding angle =65°= 65°; alternate interior angle =65°= 65°.

Answer

Corresponding angle =65°= 65°; Alternate interior angle =65°= 65°.
When a transversal crosses parallel lines, three types of angle pairs are equal: corresponding angles (same position), alternate interior angles (between the parallels, opposite sides), and alternate exterior angles (outside the parallels, opposite sides). Co-interior (same-side interior) angles are supplementary, summing to 180°.

About Transversal Angles

When a transversal (a line that crosses two parallel lines), it creates eight angles with four special relationships: corresponding angles are equal, alternate interior angles are equal, alternate exterior angles are equal, and co-interior (same-side interior) angles are supplementary.

Learn more about Transversal Angles →

More Transversal Angles Examples

Example 2 medium

Two parallel lines are cut by a transversal. Co-interior angles (same-side interior angles) are [for

Example 3 easy

A transversal crosses two parallel lines. An alternate exterior angle is [formula]. What is the meas

Example 4 hard

Lines [formula] and [formula] are cut by a transversal. Corresponding angles are [formula] and [form

← All Transversal Angles Examples Transversal Angles Concept