Regular Polygon:
A regular polygon is a polygon with equal sides and equal angles. In a regular polygon, all interior angles are congruent, meaning they have the same measure.

Formula for Interior Angle:
To find the measure of an interior angle in a regular polygon, we can use the formula:

Interior Angle = (n-2) * 180° / n

where n represents the number of sides in the polygon.

Applying the Formula:
In this case, we have a regular polygon with 9 sides. Let's substitute the value of n into the formula to find the measure of an interior angle.

Interior Angle = (9-2) * 180° / 9
Interior Angle = 7 * 180° / 9
Interior Angle = 1260° / 9
Interior Angle = 140°

Therefore, the measure of an interior angle in a regular polygon with 9 sides is 140°.

Explanation:
To understand why the formula works, let's break it down:

1. The sum of the interior angles of any polygon is given by the formula (n-2) * 180°, where n represents the number of sides. This formula can be derived by dividing the polygon into triangles and summing their angles.

2. In a regular polygon, all interior angles are congruent, so we can divide the sum of the interior angles by the number of angles to find the measure of each angle.

3. By substituting the value of n (9) into the formula, we find that the sum of the interior angles is 1260°.

4. Since a regular polygon has equal angles, we divide the sum of the interior angles by the number of angles (9) to find the measure of each angle.

5. Simplifying the division gives us the measure of each interior angle, which is 140°.

So, the measure of an interior angle in a regular polygon with 9 sides is 140°.

40 degree