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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, base angles labeled, 48 degrees, & 23 degrees, right & left sides extended, extended left side, crosses a 4th line, parallel to the extended right side. parallel lines both cross a 5th line segment. Angles are labeled at intersections as follows: right side & left side intersection, top angle is x, left side & 4th segment intersection, exterior right, y.  right side & 5th segment intersection, interior right, z, 4th & 5th segments intersection, interior bottom, 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.