Alternate Exterior Angles

Alternate Exterior Angles

Alternate exterior angles appear when a transversal crosses two lines. They are the angles outside the two lines and on opposite sides of the transversal. When the lines are parallel, these angles are equal.

How to solve

1. Identify the transversal and the two lines it intersects.
2. Find the exterior angles: they must lie outside the pair of lines.
3. Check that they are on opposite sides of the transversal.
4. If the lines are parallel, set the two angle expressions equal.
5. Solve the equation and simplify the final answer.

Example strategy

If one alternate exterior angle is given as an expression such as 3x + 7 and the matching angle is 5x - 9, write: 3x + 7 = 5x - 9 Then solve for the variable. After finding the value, substitute it back to verify both angle measures match.

Check your work

• The angles should be outside the two lines.
• They should be on opposite sides of the transversal.
• If the lines are parallel, the two measures should be the same.

A quick visual check helps prevent mixing alternate exterior angles with corresponding or alternate interior angles.