figure cdef is a parallelogram.
which equations are correct? select three options.
n = 10
n = 7
cf = 59
fe = 42
cd = 30

Question

figure cdef is a parallelogram.
which equations are correct? select three options.
  n = 10
  n = 7
  cf = 59
  fe = 42
  cd = 30

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": [ "Properties of Parallelograms", "Solving Linear Equations" ], "new_concepts": [], "current_concepts": [ "Properties of Parallelograms", "Solving Linear Equations" ] } ## Equate opposite sides of the parallelogram Using the *Properties of Parallelograms* knowledge point $$ \begin{aligned} &CF = DE\ &6n - 1 = 5n + 9 \end{aligned} $$ ## Solve for the variable n Using the *Solving Linear Equations* knowledge point $$ \begin{aligned} &(6n - 1) - 5n = (5n + 9) - 5n\ &n - 1 = 9\ &n = 10 \end{aligned} $$ ## Calculate the side lengths Using the *Properties of Parallelograms* knowledge point $$ \begin{aligned} &CF = 6(10) - 1 = 59\ &CD = 4(10) + 2 = 42\ &FE = CD = 42 \end{aligned} $$ ## Identify the correct options Using the *Properties of Parallelograms* knowledge point $$ \begin{aligned} &n = 10 \quad \text{(Correct)}\ &CF = 59 \quad \text{(Correct)}\ &FE = 42 \quad \text{(Correct)} \end{aligned} $$

n = 10

n = 7

CF = 59

FE = 42

CD = 30

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Properties of Parallelograms" ] }

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QUESTION IMAGE

Question

Explanation:

Equate opposite sides of the parallelogram

Solve for the variable n

Calculate the side lengths

Identify the correct options

Answer: