In the given figure, AB is parallel to CD. What is the value of y° − x°?

Concept

When a transversal cuts two parallel lines, corresponding angles are equal. Adjacent angles on a straight line form a linear pair and therefore sum to 180°.

Application

1. For transversal PQ, the angle corresponding to 110° at line CD is also 110°. Angle y is adjacent to it on the straight line CD, so y = 180° − 110° = 70°.

2. For transversal MN, the angle corresponding to 120° at line AB is also 120°. Angle x is adjacent to it on the straight line AB, so x = 180° − 120° = 60°.

Cross-check

The checks y + 110° = 180° and x + 120° = 180° both satisfy the linear-pair rule.

Therefore, y° − x° = 70° − 60° = 10°.