Math Problem Statement

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°

Solution

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

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

where nn is the number of sides of the polygon.

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

Exterior Angle=3609=40\text{Exterior Angle} = \frac{360^\circ}{9} = 40^\circ

Thus, the exterior angle for a regular polygon with 9 sides is 4040^\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 180180^\circ.

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Math Problem Analysis

Mathematical Concepts

Geometry
Polygons

Formulas

Exterior Angle of a Regular Polygon: 360° / n

Theorems

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Suitable Grade Level

Grades 7-9