http://www.ck12.org Chapter 3. Parallel and Perpendicular Lines
( 4 x− 10 )◦= 58 ◦
4 x= 68 ◦
x= 17 ◦Alternate Exterior Angles Theorem
Example 5:Findm^6 1 andm^6 3.
Solution:m^61 = 47 ◦because they are vertical angles. Because the lines are parallel,m^63 = 47 ◦by the Correspond-
ing Angles Theorem. Therefore,m^62 = 47 ◦.
(^6) 1 and (^6) 3 are alternate exterior angles.
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 and you will be asked to
do in the exercises at the end of this section.
Example 6:Algebra ConnectionFind the measure of each angle and the value ofy.
Solution: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