Math Problem Statement
Solution
The image shows a Geometric Jeopardy question asking for the sum and individual measurements of the angles in a regular hexagon. The options provided are:
- Total is 630° and individual is 95°.
- Total is 720° and individual is 128°.
- Total is 740° and individual is 130°.
- Total is 580° and individual is 65°.
Solution:
To solve this, we need to calculate the interior angles of a regular hexagon.
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Sum of Interior Angles: The formula to find the sum of interior angles for any polygon is: where is the number of sides. For a hexagon, : Therefore, the total sum of the interior angles is 720°.
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Individual Angle: For a regular hexagon, all interior angles are equal. The measure of each interior angle is:
The closest correct answer from the options is "Total is 720° and individual is 128°", though the individual angle provided here is incorrect (it should be 120°).
Do you want further explanation or details? Here are five related questions to expand your understanding:
- How do we find the exterior angles of a regular polygon?
- What is the sum of exterior angles for any polygon?
- How can you verify if a polygon is regular or irregular based on angle measures?
- Why is the formula for interior angle sum ?
- How would the calculations change if the hexagon were irregular?
Tip: Always remember that in any polygon, the sum of exterior angles is always 360°, regardless of the number of sides!
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Math Problem Analysis
Mathematical Concepts
Geometry
Polygon Interior Angles
Regular Polygons
Formulas
Sum of Interior Angles of a polygon: Sum = 180(n - 2)
Individual Angle of a Regular Polygon: Individual Angle = Sum / n
Theorems
Polygon Interior Angle Sum Theorem
Suitable Grade Level
Grades 8-10