Math Problem Statement

Find the sum and individual measurements of the angles in a regular hexagon. Options: - 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

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.

  1. Sum of Interior Angles: The formula to find the sum of interior angles for any polygon is: Sum=180(n2)\text{Sum} = 180(n-2) where nn is the number of sides. For a hexagon, n=6n = 6: Sum=180(62)=180×4=720\text{Sum} = 180(6-2) = 180 \times 4 = 720^\circ Therefore, the total sum of the interior angles is 720°.

  2. Individual Angle: For a regular hexagon, all interior angles are equal. The measure of each interior angle is: Individual Angle=Sumn=7206=120\text{Individual Angle} = \frac{\text{Sum}}{n} = \frac{720^\circ}{6} = 120^\circ

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:

  1. How do we find the exterior angles of a regular polygon?
  2. What is the sum of exterior angles for any polygon?
  3. How can you verify if a polygon is regular or irregular based on angle measures?
  4. Why is the formula for interior angle sum 180(n2)180(n-2)?
  5. 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