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.

images-q=tbn-ANd9GcR3YtgUWyJ0im-MwhivaIe_VWfJnhx4oJyYHfFGGnYxAxe91J-byg

Example: Identify the alternate exterior angles in the figure:
altex.png

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.

Still need help with Alternate Exterior Angles? Download Yup and get help from an expert math tutor 24/7.