# Alternate Exterior Angles

Definition: If two lines are intersected by a transversal (third line):
Alternate exterior angles are located outside the pair of lines and on opposite sides of the transversal. When the two lines crossed by a transversal are parallel, the alternate exterior angles are equal.

Example: Identify the alternate exterior angles in the figure:

Solution:

Use the definition to identify pairs of alternate exterior angles.

Step 1: We know alternate exterior angles are located “outside” a pair of lines. In this figure, the pair of lines is Line l and Line m. Keeping this in mind, we can narrow our angles down to angles ∠1, ∠2, ∠7 and ∠8, because they are all on the outside or exterior or our pair of lines, l and m.

Step 2: The definition also tells us that alternate exterior angles are located on opposite sides of the transversal (intersecting line), which here is Line t. Looking again at our exterior angles, ∠1 , ∠2, ∠7 and ∠8, we can form two pairs of angles that fit this description of being on opposite sides of the transversal.

Step 3: Based on this definition of alternate exterior angles, we can identify two pairs from the figure:

∠1 and ∠8 are alternate exterior angles because they are are on opposite sides of the transversal, and are outside the pair of lines.
∠2 and ∠7 are alternate exterior angles because they are are on opposite sides of the transversal, and are outside the pair of lines.

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