Example 3

In the following diagram, and . If , , and , find the measures of the unknown angles and the values of and .
  1. Find the relationship between two angles that have the same variable.
  2. Use the Same-Side Interior Angles Theorem.
  3. Use substitution and solve for .
  4. Find and using substitution.
  5. Find the relationship between one of the known angles and the last unknown angle, .
  6. Use the Alternate Interior Angles Theorem.
  7. Use the definition of congruence and substitution to find .
  8. 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.