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? \\(\square\\)° what is the angle between the west path and willow lane? \\(\square\\)°

Explanation:

Step1: Identify the trapezoid type

The park is a trapezoid with Main Street and Willow Lane parallel, and east and west paths equal in length, so it's an isosceles trapezoid. In an isosceles trapezoid, base angles are equal, and consecutive angles between the bases are supplementary (sum to \(180^\circ\)).

Step2: Find angle between Main Street and west path

The angle between Willow Lane and east path is \(60^\circ\). In an isosceles trapezoid, the angle between Main Street (top base) and west path is supplementary to the angle between Willow Lane (bottom base) and east path. So, \(180^\circ - 60^\circ = 120^\circ\).

Step3: Find angle between west path and Willow Lane

Since it's an isosceles trapezoid, the angle between west path and Willow Lane is equal to the angle between east path and Willow Lane, which is \(60^\circ\).

Answer:

Angle between Main Street and west path: \(120^\circ\)
Angle between west path and Willow Lane: \(60^\circ\)