given the diagram below, what is $m\angle d$?

a. $74^\circ$
b. $72^\circ$
c. $108^\circ$
d. $68^\circ$

Question

given the diagram below, what is $m\angle d$?

a. $74^\circ$
b. $72^\circ$
c. $108^\circ$
d. $68^\circ$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Isosceles Trapezoid Properties" ], "new_concepts": [], "current_concepts": [ "Isosceles Trapezoid Properties", "Consecutive Interior Angles" ] } ## Identify the properties of the quadrilateral $$ \begin{aligned} &m\angle B = 108^\circ \ &m\angle C = 108^\circ \ &m\angle A = 72^\circ \ &m\angle B + m\angle A = 108^\circ + 72^\circ = 180^\circ \implies BC \parallel AD \end{aligned} $$ ## Calculate the measure of angle D $$ \begin{aligned} &m\angle A + m\angle B + m\angle C + m\angle D = 360^\circ \ &72^\circ + 108^\circ + 108^\circ + m\angle D = 360^\circ \ &288^\circ + m\angle D = 360^\circ \ &m\angle D = 72^\circ \end{aligned} $$

A. $74^\circ$

B. $72^\circ$

C. $108^\circ$

D. $68^\circ$

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

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QUESTION IMAGE

Question

Explanation:

Identify the properties of the quadrilateral

Calculate the measure of angle D

Answer: