fiona drew a regular polygon that first maps directly onto itself after rotating 15 degrees. how many sides does the polygon have?

12
15
24
48

Question

fiona drew a regular polygon that first maps directly onto itself after rotating 15 degrees. how many sides does the polygon have?

12
15
24
48

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Rotational Transformations" ], "new_concepts": [ "Rotational Symmetry of Regular Polygons" ], "current_concepts": [ "Rotational Transformations", "Rotational Symmetry of Regular Polygons" ] } ## Identify the relationship between rotation angle and number of sides $$ \theta = \frac{360^\circ}{n} $$ ## Substitute the given minimum rotation angle $$ 15^\circ = \frac{360^\circ}{n} $$ ## Solve for the number of sides $$ n = \frac{360^\circ}{15^\circ} = 24 $$

12

15

24

48

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Rotational Symmetry of Regular Polygons" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the relationship between rotation angle and number of sides

Substitute the given minimum rotation angle

Solve for the number of sides

Answer: