The measurement of each internal angle of a regular polygon is 120°. How many sides does it have?Group of answer choices5 sides6 sides8 sides
Question
The measurement of each internal angle of a regular polygon is 120°. How many sides does it have?
Group of answer choices
- 5 sides
- 6 sides
- 8 sides
Solution
1. ### Break Down the Problem
To find the number of sides in a regular polygon where each internal angle measures , we need to use the formula for the internal angle of a regular polygon, which is:
where is the number of sides.
2. ### Relevant Concepts
We know:
- Given internal angle = .
- Set the equation for internal angle equal to and solve for .
3. ### Analysis and Detail
Setting up the equation:
Multiplying both sides by :
Expanding the right side:
Rearranging to isolate :
4. ### Verify and Summarize
To verify, we can substitute back into the internal angle formula:
This verifies our solution is correct.
Final Answer
The regular polygon has 6 sides.
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The measure of an interior angle of a regular polygon is 156°. Find the number of sides in the polygon.
Each exterior angle of a regular polygon measures 9°. How many sides does the polygon have?Choices:- 36 45 40 30
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