the sum of the measures of the interior angles of a polygon is $2880^{\circ}$. how many sides does the polygon have?

14
16
18
20

Question

the sum of the measures of the interior angles of a polygon is $2880^{\circ}$. how many sides does the polygon have?

14
16
18
20

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Polygon Interior Angles Theorem", "Interior Angle Sum Formula" ], "current_concepts": [ "Polygon Interior Angles Theorem", "Interior Angle Sum Formula" ] } ## Set up the interior angle sum equation $$ (n - 2) \times 180^\circ = 2880^\circ $$ ## Solve for n $$ \begin{aligned} n - 2 &= \frac{2880}{180} \ n - 2 &= 16 \ n &= 18 \end{aligned} $$

(A) 14

(B) 16

(C) 18

(D) 20

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Polygon Interior Angles Theorem" ] }

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Question

Explanation:

Set up the interior angle sum equation

Solve for n

Answer: