3.5. Alternate Exterior Angles http://www.ck12.org
Example A
Using the picture above, list all the pairs of alternate exterior angles.
Alternate Exterior Angles:^6 2 and^6 7,^6 1 and^6 8.
Example B
Findm^6 1 andm^6 3.
m^61 = 47 ◦because they are vertical angles. Because the lines are parallel,m^63 = 47 ◦by the Corresponding Angles
Theorem. Therefore,m^62 = 47 ◦.
(^6) 1 and (^6) 3 are alternate exterior angles.
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 130◦angle and^6 aare alternate exterior angles. Ifm^6 a= 130 ◦, then the lines are parallel. To findm^6 a,
use the other labeled angle which is 40◦, and its linear pair. Therefore,^6 a+ 40 ◦= 180 ◦and^6 a= 140 ◦. 140◦ 6 = 130 ◦,
so Franklin Way and Chavez Avenue arenot parallel streets.
Watch this video for help with the Examples above.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter3AlternateExteriorAnglesB
Vocabulary
Alternate Exterior Anglesare two angles that are on theexterior oflandm, but on opposite sides of the transversal.
Guided Practice
- Find the measure of each angle and the value ofy.
- Give THREE examples of pairs of alternate exterior angles in the diagram below:
Answers:
- 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.
( 3 y+ 53 )◦= ( 7 y− 55 )◦
108 ◦= 4 y
27 ◦=y