Question

A town planner wants to build two new streets, Elm Street and Garden Road, to connect parallel streets Maple Drive and Pine Avenue. Trapezoid E F G H is shown. F G is Maple Drive, G H is Garden road, E H is Pine avenue, and E F is Elm Street. Sides F G and E H are parallel. Angle G is 108 degrees. In trapezoid EFGH, EF ≅ HG. What is the measure of the angle between Elm Street and Pine Avenue? 54° 72° 108° 144°

Answer 1

B. 72

Explanation:

Answer 2

72°

Explanation:

From the information given:

A town planner wants to build two new streets, Elm Street and Garden Road, to connect parallel streets Maple Drive and Pine Avenue.

We are also told that there is a Trapezoid EFGH with EH as the Pine avenue and EF as the Elm street.

However, side FG and EH are parallel.

∠G = 108°

From the property of parallel lines :

since FG || EH

Then ∠G = ∠H = 108° (i.e corresponding angle will also be equal)

The required angle between Elm Street and Pine Avenue would be interior angles + 180° given that alternate angles are also equal.

The required angle between Elm Street and Pine Avenue = 180° - 108°

The required angle between Elm Street and Pine Avenue = 72°