To find the size of each interior angle of a regular 12-gon (dodecagon), we will follow these steps:
1. Understand the Problem: We need to determine the measure of each interior angle of a regular 12-sided polygon, known as a dodecagon.
2. Calculate the Sum of Interior Angles:
- The formula to find the sum of the interior angles of an n-sided polygon is [tex]\((n - 2) \times 180^\circ\)[/tex], where [tex]\(n\)[/tex] is the number of sides.
- For a regular 12-gon: [tex]\(n = 12\)[/tex].
- Sum of interior angles [tex]\(= (12 - 2) \times 180^\circ\)[/tex].
3. Perform the Calculation:
- Subtract 2 from the number of sides: [tex]\(12 - 2 = 10\)[/tex].
- Multiply the result by 180°: [tex]\(10 \times 180^\circ = 1800^\circ\)[/tex].
4. Determine Each Interior Angle:
- A regular polygon has all its interior angles equal.
- To find the measure of each interior angle, divide the sum of the interior angles by the number of sides.
- Each interior angle [tex]\(= \frac{\text{Sum of interior angles}}{n}\)[/tex].
- Each interior angle [tex]\(= \frac{1800^\circ}{12}\)[/tex].
5. Perform the Division:
- [tex]\( \frac{1800^\circ}{12} = 150^\circ \)[/tex].
Therefore, the size of each interior angle of a regular 12-gon is [tex]\(150^\circ\)[/tex].
In summary, the sum of the interior angles of a regular 12-gon is [tex]\(1800^\circ\)[/tex], and each interior angle is [tex]\(150^\circ\)[/tex].
