Question

city planners want to design a park between parallel streets, main street and willow lane, in the shape of a trapezoid. there are two paths of equal length on the east and west sides of the park. the border of the park makes a 60° angle between willow lane and the east path. what is the angle between main street and the west path? what is the angle between the west path and willow lane? 60 120 240 360

Explanation:

Step1: Use property of parallel lines

Since Main Street and Willow Lane are parallel, and the trapezoid - shaped park is formed between them. The east and west paths are of equal length. The angle between Willow Lane and the east path is 60°.

Step2: Find angle between Main Street and west path

The angle between Main Street and the west path is 60° because of the corresponding - angles property for parallel lines. When two parallel lines (Main Street and Willow Lane) are intersected by a transversal (the west path), the corresponding angles are equal.

Step3: Find angle between west path and Willow Lane

The angle between the west path and Willow Lane is 120° because the sum of adjacent angles on the same side of a transversal between two parallel lines is 180°. If one of the adjacent angles is 60°, then the other is 180 - 60=120°.

Answer:

What is the angle between Main Street and the west path? 60°
What is the angle between the west path and Willow Lane? 120°