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, $\overline{ef} \cong \overline{hg}$. what is the measure of the angle between elm street and pine avenue?

$54^\circ$
$72^\circ$
$108^\circ$
$144^\circ$

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, $\overline{ef} \cong \overline{hg}$. what is the measure of the angle between elm street and pine avenue?

$54^\circ$
$72^\circ$
$108^\circ$
$144^\circ$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Isosceles Trapezoid Base Angles Theorem", "Consecutive Interior Angles" ], "new_concepts": [], "current_concepts": [ "Isosceles Trapezoid Base Angles Theorem", "Consecutive Interior Angles", "Trapezoid Properties" ] } ## Identify the properties of the trapezoid Using the *Isosceles Trapezoid Base Angles Theorem* knowledge point $$ \begin{aligned} &\overline{EF} \cong \overline{HG} \implies EFGH \text{ is an isosceles trapezoid}\ &\angle F \cong \angle G \implies m\angle F = m\angle G = 108^\circ \end{aligned} $$ ## Calculate the angle between Elm Street and Pine Avenue Using the *Consecutive Interior Angles* knowledge point $$ \begin{aligned} &\overline{FG} \parallel \overline{EH} \implies m\angle E + m\angle F = 180^\circ\ &m\angle E + 108^\circ = 180^\circ\ &m\angle E = 72^\circ \end{aligned} $$

54°

72°

108°

144°

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Isosceles Trapezoid Base Angles Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the properties of the trapezoid

Calculate the angle between Elm Street and Pine Avenue

Answer: