In a regular polygon, if the measure of each exterior angle is 30 degrees, how m

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Question: In a regular polygon, if the measure of each exterior angle is 30 degrees, how many sides does the polygon have? (2023)

Options:

Correct Answer: 6

Exam Year: 2023

Solution:

The measure of each exterior angle of a regular polygon is given by 360/n. Setting 360/n = 30 gives n = 12.

In a regular polygon, if the measure of each exterior angle is 30 degrees, how many sides does the polygon have? (2023)

In a regular polygon, if the measure of each exterior angle is 30 degrees, how many sides does the polygon have? (2023)

Step 1: Understand that the exterior angle of a regular polygon can be calculated using the formula: 360/n, where n is the number of sides.
Step 2: We know from the question that each exterior angle measures 30 degrees.
Step 3: Set up the equation using the formula: 360/n = 30.
Step 4: To find n, we need to rearrange the equation. Multiply both sides by n: 360 = 30n.
Step 5: Now, divide both sides by 30 to solve for n: n = 360/30.
Step 6: Calculate the right side: n = 12.

Exterior Angles of Polygons – The measure of each exterior angle of a regular polygon can be calculated using the formula 360/n, where n is the number of sides.
Regular Polygons – A regular polygon is a polygon with all sides and angles equal, which allows for the use of uniform formulas for angle measures.