Question

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, $overline{ef}=overline{hg}$. what is the measure of the angle between elm street and pine avenue? 54° 72° 108° 144°

Explanation:

Step1: Recall property of trapezoid

In an isosceles trapezoid (since $\overline{EF}=\overline{HG}$), base - angles are equal and consecutive angles between parallel lines are supplementary.

Step2: Identify relevant angles

Maple Drive and Pine Avenue are parallel. The angle adjacent to the $108^{\circ}$ angle 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 $x$. Since consecutive - interior angles between parallel lines add up to $180^{\circ}$, we have $x + 108^{\circ}=180^{\circ}$. Solving for $x$, we get $x=180^{\circ}- 108^{\circ}=72^{\circ}$.

Answer:

$72^{\circ}$