city planners want to design a park between parallel streets, main street and willow lane, in the shape of a…

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?

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?

Answer

Explanation:

Step1: Use property of isosceles trapezoid

In an isosceles trapezoid, base - angles are equal.

Step2: Determine angle between Main Street and west path

Since the trapezoid is formed between parallel streets and the east - west paths are of equal length (isosceles trapezoid), the angle between Main Street and the west path is equal to the angle between Willow Lane and the east path. So it is $60^{\circ}$.

Step3: Determine angle between west path and Willow Lane

The angle between the west path and Willow Lane is also equal to the angle between the east path and Willow Lane due to the isosceles - trapezoid property. So it is $60^{\circ}$.

Answer:

What is the angle between Main Street and the west path? $60^{\circ}$ What is the angle between the west path and Willow Lane? $60^{\circ}$