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 { e f } \cong \overline { h g } \\). what is the measure of the angle between elm street and pine avenue? 54° 72° 108° 144°

Explanation:

Step1: Identify the trapezoid type

Since \( \overline{EF}\cong\overline{HG}\), trapezoid \(EFGH\) is isosceles. In an isosceles trapezoid, consecutive - interior angles between the non - parallel sides and the parallel sides are supplementary. Let the angle between Elm Street (\(EF\)) and Pine Avenue (\(EH\)) be \(x\). The given angle is \(108^{\circ}\) (angle between \(HG\) and \(GH\)).

Step2: Use the supplementary - angle property

For parallel lines (Maple Dr and Pine Ave) and the transversals (Elm St and Garden Rd), we know that \(x + 108^{\circ}=180^{\circ}\) (supplementary angles). Solving for \(x\), we get \(x = 180^{\circ}-108^{\circ}\).

Answer:

\(72^{\circ}\)