If the exterior angle of a regular polygon is 30 degrees, how many sides does it

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Question: If the exterior angle of a regular polygon is 30 degrees, how many sides does it have?

Options:

Correct Answer: 12

Solution:

The sum of the exterior angles of any polygon is 360 degrees. Therefore, the number of sides can be calculated as 360 / 30 = 12.

If the exterior angle of a regular polygon is 30 degrees, how many sides does it have?

If the exterior angle of a regular polygon is 30 degrees, how many sides does it have?

Step 1: Understand that the exterior angle of a polygon is the angle formed between one side of the polygon and the extension of an adjacent side.
Step 2: Know that the sum of all exterior angles of any polygon is always 360 degrees.
Step 3: Since the polygon is regular, all exterior angles are equal. In this case, each exterior angle is given as 30 degrees.
Step 4: To find the number of sides of the polygon, divide the total sum of the exterior angles (360 degrees) by the measure of one exterior angle (30 degrees).
Step 5: Perform the calculation: 360 divided by 30 equals 12.
Step 6: Conclude that the polygon has 12 sides.

Exterior Angles of Polygons – The exterior angle of a polygon is formed by one side of the polygon and the extension of an adjacent side. The sum of all exterior angles of any polygon is always 360 degrees.
Regular Polygons – A regular polygon is a polygon with all sides and angles equal. The measure of each exterior angle can be found by dividing 360 degrees by the number of sides.