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: Identify the trapezoid type

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

Step2: Recall angle - sum property of trapezoid

In a trapezoid with parallel bases, the sum of the angles on the same - side of a non - parallel side is $180^{\circ}$. Maple Drive and Pine Avenue are parallel. The angle adjacent to the $108^{\circ}$ angle on the same non - parallel side (Garden Road) and the $108^{\circ}$ angle are supplementary. Let the angle between Elm Street and Pine Avenue be $x$.

Step3: Calculate the angle

We know that $x + 108^{\circ}=180^{\circ}$. Solving for $x$, we get $x = 180^{\circ}-108^{\circ}=72^{\circ}$.

Answer:

$72^{\circ}$