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To find the measure of an interior angle of a regular decagon (a polygon with 10 sides), we can use the formula for the sum of interior angles of a polygon:

\[
\text{Sum of interior angles} = (n - 2) \times 180^\circ
\]

where \( n \) is the number of sides. For a decagon, \( n = 10 \):

\[
\text{Sum of interior angles} = (10 - 2) \times 180^\circ = 8 \times 180^\circ = 1440^\circ
\]

Next, to find the measure of one interior angle in a regular polygon, we divide the total sum by the number of sides:

\[
\text{Measure of one interior angle} = \frac{1440^\circ}{10} = 144^\circ
\]

Thus, each interior angle of a regular decagon measures **144°**.

Would you like more details on this process or have any questions?

Here are 5 related questions for further exploration:
1. How do you calculate the exterior angle of a regular polygon?
2. What is the sum of the exterior angles of any polygon?
3. How does the number of sides of a polygon affect the measure of its interior angles?
4. How do you calculate the measure of an interior angle for polygons with a different number of sides, such as a pentagon or octagon?
5. What is the relationship between interior and exterior angles in regular polygons?

**Tip**: For any regular polygon, the sum of the exterior angles is always \( 360^\circ \), regardless of the number of sides.

Find the measure of an interior angle of a regular decagon (10-sided polygon).

Learn how to calculate the interior angle of a regular decagon with 10 sides using the sum of interior angles formula. This geometric problem includes key concepts such as the Polygon Angle Sum Theorem and is suitable for students in Grades 8-10.

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