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?

°

Answer 1

The first one is 120
the second one is 60

Answer 2

A) The angle between Main Street and the west path is 120°.

B) The angle between the west path and Willow Lane is 60°

See the picture attached for reference.

We know that Willow Lane and Main Street are parallel, therefore they form the two bases of the trapezoid (AB and CD).

We also know that the two legs (AD and BC) are the West and the East paths and they have the same length. Therefore ours is an isosceles trapezoid.

We know that ∡B = angle between Willow Lane and the East path is 60°.

A generic trapezoid has the following property:
- adjacent angles to opposite bases are supplementary:
∠A + ∠D = 180°
∠B + ∠C = 180°

An isosceles trapezoid has the following property:
- the base angles are congruent:
∠A ≡ ∠B and ∠C ≡ ∠D

Knowing that ∡B = 60°, using the above properties, we can say that:
∡A = ∡B = 60°
∡D = 180° - ∡A = 180° - 60° = 120°
∡C = 180° - ∡B = 180° - 60° = 120°
or else,
∡C = ∡D = 120°

Therefore:
A) ∠D = angle between Main Street and the west path = 120°.

B) ∠A = angle between the west path and Willow Lane = 60°