Find the exterior angle for a regular polygon with 9 sides.

أوجد قياس الزاوية الخارجية لمضلع منتظم ذي 9 أضلاع   

A.

40°

B.

30°

C.

20°

D.

10°

The exterior angle of a regular polygon can be found using the formula:

\[
\text{Exterior Angle} = \frac{360^\circ}{n}
\]

where \( n \) is the number of sides of the polygon.

Given that the polygon has 9 sides, we can substitute \( n = 9 \) into the formula:

\[
\text{Exterior Angle} = \frac{360^\circ}{9} = 40^\circ
\]

Thus, the exterior angle for a regular polygon with 9 sides is \( 40^\circ \).

The correct answer is **A. 40°**.

Would you like more details or have any questions about this? 

Here are some related questions:

1. How do the interior and exterior angles of a regular polygon relate to each other?
2. What is the sum of the interior angles for a polygon with 9 sides?
3. Can a regular polygon have an exterior angle less than 10°?
4. How many diagonals does a polygon with 9 sides have?
5. What is the name of a polygon with 9 sides?
6. If the exterior angle of a polygon is 30°, how many sides does it have?
7. What is the formula for finding the interior angle given the number of sides?
8. How does the exterior angle change as the number of sides increases?

**Tip:** The exterior angle and the interior angle of a regular polygon are complementary, meaning they add up to \( 180^\circ \).

Learn how to find the exterior angle of a regular polygon with 9 sides using the formula: Exterior Angle = 360° / n. This problem explores geometric concepts related to polygons and angles. Suitable for students in Grades 7-9.

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