a town planner wants to build two new streets, elm street and garden road, to connect parallel streets maple…

a town planner wants to build two new streets, elm street and garden road, to connect parallel streets maple drive and pine avenue. in trapezoid efgh, $overline{ef}congoverline{hg}$. what is the measure of the angle between elm street and pine avenue? 54° 72° 108° 144°

a town planner wants to build two new streets, elm street and garden road, to connect parallel streets maple drive and pine avenue. in trapezoid efgh, $overline{ef}congoverline{hg}$. what is the measure of the angle between elm street and pine avenue? 54° 72° 108° 144°

Answer

Explanation:

Step1: Identify the trapezoid type

Since $\overline{EF}\cong\overline{HG}$, trapezoid $EFGH$ is an isosceles trapezoid.

Step2: Recall angle - property of isosceles trapezoid

In an isosceles trapezoid, base - angles are equal and consecutive interior angles between parallel lines are supplementary. Maple Drive and Pine Avenue are parallel. The angle at $G$ and the angle between Elm Street and Pine Avenue are consecutive interior angles.

Step3: Calculate the required angle

Let the angle between Elm Street and Pine Avenue be $\theta$. We know that if one of the consecutive interior angles is $108^{\circ}$, then $\theta + 108^{\circ}=180^{\circ}$ (because consecutive interior angles between parallel lines are supplementary). Solving for $\theta$, we get $\theta=180^{\circ}- 108^{\circ}=72^{\circ}$.

Answer:

$72^{\circ}$