To find the measure of angle ZXYZ, which is denoted as Z in the diagram and subtended by line XY, we need to understand the properties of angles formed by intersecting lines. In this case, angle ZXYZ is an alternate interior angle to the angle with a given measure of 110°.
Here's how we can identify the expression that gives the measure of angle ZXYZ:
1. Angle ZXYZ and the angle with a measure of 110° are alternate interior angles as they are on opposite sides of the transversal line XY and between the lines ZW and XY.
2. By the Alternate Interior Angle Theorem, alternate interior angles are congruent when two parallel lines are cut by a transversal, even if the lines are not parallel but the transversal is a secant line.
3. Therefore, the measure of angle ZXYZ is the same as the measure of the given angle, which is 110°.
Based on this understanding, the expression that gives the measure of ZXYZ is:
A. 110° + 42°
This expression is correct because angle ZXYZ is congruent to the given angle of 110°, making its measure 110°.
