Question

solving problems with trapezoids
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?
angle between the west path and willow lane?

Explanation:

Step1: Identify the trapezoid type

Since the two paths (legs) are equal in length, the trapezoid is isosceles.

Step2: Use the property of consecutive - interior angles in parallel lines

For parallel lines (Main Street and Willow Lane), consecutive - interior angles are supplementary. Let the angle between Main Street and the west path be \(x\), and the angle between Willow Lane and the east path be \(60^{\circ}\).
In an isosceles trapezoid, the angles adjacent to each non - parallel side are supplementary. If we consider the pair of angles formed by a path (leg) and the two parallel streets (Main Street and Willow Lane), we know that \(x + 60^{\circ}=180^{\circ}\) (consecutive - interior angles for parallel lines).

Answer:

\(120^{\circ}\)