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Learn about shapes with equal sides and angles: how many sides when the corner outside measures 30 degrees?
How many Sides does a Regular polygon have if each exterior angle measures 30?
The regular polygon has 12 sides.
To find the number of sides of a regular polygon when each exterior angle measures 30 degrees, you can use the formula for the relationship between the exterior angle of a regular polygon and the number of sides:
Number of sides = 360 / Exterior angle
Substituting the given value of the exterior angle (30 degrees):
Number of sides = 360 / 30 = 12
So, the regular polygon has 12 sides.
Finding the Number of Sides in a Regular Polygon Given the Measure of Each Exterior Angle
To find the number of sides in a regular polygon given the measure of each exterior angle, you can use the formula:
n = 360° / (measure of each exterior angle)
where:
- n is the number of sides in the polygon.
- 360° represents the total angle measure of a full rotation.
Here’s how you can apply this formula:
- Determine the measure of each exterior angle of the regular polygon.
- Substitute this value into the formula.
- Calculate the result to find the number of sides in the polygon.
Let’s go through an example:
Suppose the measure of each exterior angle of a regular polygon is 45°.
n = 360° / 45°
n = 360 / 45
n = 8
So, the regular polygon has 8 sides.
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Source: Math Hello Kitty
Categories: Math
