question 8 of 10

if efgh is a parallelogram, what is the value of x?

a. 36
b. 34
c. 37
d. 30.5
e. 82
f. 9

Question

question 8 of 10

if efgh is a parallelogram, what is the value of x?

a. 36
b. 34
c. 37
d. 30.5
e. 82
f. 9

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": [ "Parallelogram Angle Properties", "Consecutive Interior Angles" ], "new_concepts": [], "current_concepts": [ "Parallelogram Angle Properties", "Consecutive Interior Angles" ] } ## Identify the geometric relationship Using the *Parallelogram Angle Properties* and *Consecutive Interior Angles* knowledge points $$ \begin{aligned} &EFGH \text{ is a parallelogram} \implies EF \parallel HG\ &m\angle F + m\angle G = 180^\circ\ &(4x - 2)^\circ + 34^\circ = 180^\circ \end{aligned} $$ ## Solve the linear equation for x Using the *Parallelogram Angle Properties* knowledge point $$ \begin{aligned} &4x - 2 + 34 = 180\ &4x + 32 = 180\ &4x = 148\ &x = 37 \end{aligned} $$

A. 36

B. 34

C. 37

D. 30.5

E. 82

F. 9

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Parallelogram Angle Properties" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the geometric relationship

Solve the linear equation for x

Answer: