Math Problem Statement
Solution
We are asked to find the number of sides in an irregular polygon where one exterior angle is , and all other exterior angles are .
Key Concepts:
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Sum of exterior angles in a polygon: The sum of the exterior angles of any polygon is always , regardless of whether it is regular or irregular.
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Approach:
- Let be the total number of sides of the polygon.
- We know that one exterior angle is , and the remaining exterior angles are each .
Step-by-step Solution:
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The sum of all exterior angles is given by:
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Simplifying the equation:
Final Answer:
The polygon has 21 sides.
Would you like more details or have any questions? Here are some related questions to expand your understanding:
- What is the relationship between exterior angles and the number of sides in a polygon?
- How would the formula change if all the angles were equal?
- Can you explain how the sum of exterior angles is always ?
- What is the formula for finding the number of sides in a regular polygon if all exterior angles are given?
- How does the irregularity of the polygon affect the calculation?
Tip: For any polygon, the sum of exterior angles is always , whether the polygon is regular or irregular!
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Math Problem Analysis
Mathematical Concepts
Geometry
Polygons
Exterior Angles
Formulas
Sum of exterior angles of a polygon = 360°
Theorems
The sum of exterior angles of any polygon is always 360°
Suitable Grade Level
Grades 9-12
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