Kirk Perkins
02/13/2023 · High School
In a regular polygon with 6 sides, the sum of all the angles is and every internal angle measures In a regular polygon with 8 sides, the sum of all the angles is and every internal angle measures
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Step-by-step Solution
To find the sum of the interior angles of a regular polygon, you can use the formula:
\[
\text{Sum of interior angles} = (n - 2) \times 180^\circ
\]
where \( n \) is the number of sides of the polygon.
### For a regular polygon with 6 sides (hexagon):
1. **Sum of all angles**:
\[
\text{Sum} = (6 - 2) \times 180^\circ = 4 \times 180^\circ = 720^\circ
\]
2. **Each internal angle**:
\[
\text{Each angle} = \frac{\text{Sum}}{n} = \frac{720^\circ}{6} = 120^\circ
\]
### For a regular polygon with 8 sides (octagon):
1. **Sum of all angles**:
\[
\text{Sum} = (8 - 2) \times 180^\circ = 6 \times 180^\circ = 1080^\circ
\]
2. **Each internal angle**:
\[
\text{Each angle} = \frac{\text{Sum}}{n} = \frac{1080^\circ}{8} = 135^\circ
\]
### Summary:
- In a regular hexagon (6 sides):
- The sum of all angles is \( 720^\circ \).
- Each internal angle measures \( 120^\circ \).
- In a regular octagon (8 sides):
- The sum of all angles is \( 1080^\circ \).
- Each internal angle measures \( 135^\circ \).
Quick Answer
- In a regular hexagon (6 sides):
- The sum of all angles is \( 720^\circ \).
- Each internal angle measures \( 120^\circ \).
- In a regular octagon (8 sides):
- The sum of all angles is \( 1080^\circ \).
- Each internal angle measures \( 135^\circ \).
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