If the exterior angle of a regular polygon is 30 degrees, how many sides does it have?
Practice Questions
1 question
Q1
If the exterior angle of a regular polygon is 30 degrees, how many sides does it have?
6
12
10
8
The sum of the exterior angles of any polygon is 360 degrees. Therefore, the number of sides can be calculated as 360 / 30 = 12.
Questions & Step-by-step Solutions
1 item
Q
Q: If the exterior angle of a regular polygon is 30 degrees, how many sides does it have?
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.
Steps: 6
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.
