Example 3

In the following diagram,

and

. If

, and

, find the measures of the unknown angles and the values of

and

Find the relationship between two angles that have the same variable.
Use the Same-Side Interior Angles Theorem.
Use substitution and solve for .
Find and using substitution.
Find the relationship between one of the known angles and the last unknown angle, .
Use the Alternate Interior Angles Theorem.
Use the definition of congruence and substitution to find .
Use substitution to solve for .

This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit www.walch.com for more information.

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