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Home > CCG > Chapter 10 > Lesson 10.2.2 > Problem 10-88


Examine the diagram below. Use the given geometric relationships to solve for . Be sure to justify your work by stating the geometric relationship and applicable theorem.  

A triangle, with base angles labeled, 48 degrees, and 23 degrees, with right and left sides extended, extended left side, crosses a fourth line, parallel to the extended right side. parallel lines both cross a fifth line segment. Angles are labeled at intersections as follows: right & left, top angle is x, left & fourth, exterior right, y,  right & fifth, interior right, z, fourth & fifth, interior left, 81 degrees.

Use the Triangle Angle Sum Theorem to find .

Angles added: intersection left & right, bottom labeled theta, intersection of left & fourth, exterior left labeled, alpha.

Vertical angles are equal. Use this information to find .

When solving for , remember that parallel lines have equal corresponding angles.