3.5: Alternate Exterior Angles
What if you were presented with two angles that are on opposite sides of a transversal, but outside the lines? How would you describe these angles and what could you conclude about their measures? After completing this Concept, you'll be able to answer these questions using your knowledge of alternate exterior angles.
Watch This
CK12 Foundation: Chapter3AlternateExteriorAnglesA
Watch the portions of this video dealing with alternate exterior angles.
James Sousa: Angles and Transversals
James Sousa: Proof of Alternate Exterior Angles Converse
Guidance
Alternate Exterior Angles are two angles that are on the exterior of
Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal, then the alternate exterior angles are congruent.
The proof of this theorem is very similar to that of the Alternate Interior Angles Theorem.
Converse of the Alternate Exterior Angles Theorem: If two lines are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel.
Example A
Using the picture above, list all the pairs of alternate exterior angles.
Alternate Exterior Angles:
Example B
Find
Example C
The map below shows three roads in Julio’s town.
Julio used a surveying tool to measure two angles at the intersections in this picture he drew (NOT to scale). Julio wants to know if Franklin Way is parallel to Chavez Avenue.
The labeled
Watch this video for help with the Examples above.
CK12 Foundation: Chapter3AlternateExteriorAnglesB
Vocabulary
Alternate Exterior Angles are two angles that are on the exterior of
Guided Practice
1. Find the measure of each angle and the value of
2. Give THREE examples of pairs of alternate exterior angles in the diagram below:
Answers:
1. The given angles are alternate exterior angles. Because the lines are parallel, we can set the expressions equal to each other to solve the problem.
If
2. There are many examples of alternate exterior angles in the diagram. Here are some possible answers:

∠1 and∠14

∠2 and∠13

∠12 and∠13
Practice
 Find the value of
x ifm∠1=(4x+35)∘, m∠8=(7x−40)∘ :  Are lines 1 and 2 parallel? Why or why not?
For 36, what does the value of

m∠2=(8x)∘ andm∠7=(11x−36)∘ 
m∠1=(3x+5)∘ andm∠8=(4x−3)∘ 
m∠2=(6x−4)∘ andm∠7=(5x+10)∘ 
m∠1=(2x−5)∘ andm∠8=(x)∘ 
m∠2=(3x+50)∘ andm∠7=(10x+1)∘ 
m∠1=(2x−12)∘ andm∠8=(x+1)∘
For 912, determine whether the statement is true or false.
 Alternate exterior angles are always congruent.
 If alternate exterior angles are congruent then lines are parallel.
 Alternate exterior angles are on the interior of two lines.
 Alternate exterior angles are on opposite sides of the transversal.
For questions 1315, use the picture below.
 What is the alternate exterior angle with
∠2 ?  What is the alternate exterior angle with
∠7 ?  Are the two lines parallel? Explain.
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Image Attributions
Here you'll learn what alternate exterior angles are and their relationship with parallel lines.