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

There are some other angles in the diagram that have the same measures as and . Which ones?

Added to the diagram, Intersection of left & right sides, bottom angle labeled, x, right angle, labeled, y. Intersection of left side & fourth line, interior left angle, labeled, y, bottom exterior angle labeled, x.