# Example 3

- Author:
- Walch Education

- Topic:
- Angles

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
.