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In a certain polygon, if the exterior angle is 30 degrees, how many sides does t

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

Options:

  1. 6
  2. 8
  3. 12
  4. 10

Correct Answer: 6

Exam Year: 2023

Solution: 

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

In a certain polygon, if the exterior angle is 30 degrees, how many sides does t

Practice Questions

Q1
In a certain polygon, if the exterior angle is 30 degrees, how many sides does the polygon have? (2023)
  1. 6
  2. 8
  3. 12
  4. 10

Questions & Step-by-Step Solutions

In a certain polygon, if the exterior angle is 30 degrees, how many sides does the polygon have? (2023)
  • Step 1: Understand that the sum of all exterior angles of any polygon is always 360 degrees.
  • Step 2: Know that each exterior angle of the polygon is given as 30 degrees.
  • Step 3: To find the number of sides (n) of the polygon, use the formula: n = 360 degrees / exterior angle.
  • Step 4: Substitute the exterior angle into the formula: n = 360 / 30.
  • Step 5: Calculate the result: n = 12.
  • Exterior Angles of Polygons – The exterior angle of a polygon is the angle formed between 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.
  • Calculating Number of Sides – The number of sides of a polygon can be calculated by dividing the total sum of exterior angles (360 degrees) by the measure of one exterior angle.
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