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If the sum of the interior angles of a regular polygon is 540o then how many sides does it have?
- a)6
- b)8
- c)5
- d)9
Correct answer is option 'C'. Can you explain this answer?
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If the sum of the interior angles of a regular polygon is 540othen how...
Let the regular polygon has n sides. We also know that the sum of all the interior angles of a regualr polygon with n sides is (n - 2) × 180°
According to the question,
⇒ (n - 2) × 180° = 540°
⇒ n - 2 = 3
∴ n = 5
Most Upvoted Answer
If the sum of the interior angles of a regular polygon is 540othen how...
Understanding the Sum of Interior Angles
The formula to calculate the sum of the interior angles of a polygon is:
- Sum of interior angles = (n - 2) × 180
Where "n" is the number of sides in the polygon.
Given Information
In this case, the sum of the interior angles is given as 540 degrees.
Setting Up the Equation
We can set up the equation based on the formula:
- (n - 2) × 180 = 540
Simplifying the Equation
To find "n", we can simplify the equation:
1. Divide both sides by 180:
- n - 2 = 540 / 180
- n - 2 = 3
2. Solve for n:
- n = 3 + 2
- n = 5
Conclusion
The value of n is 5, which indicates that the polygon is a pentagon. Therefore, the correct answer is option 'C', which represents a polygon with 5 sides.
Key Points to Remember
- The sum of the interior angles can help determine the number of sides.
- A polygon with 5 sides is called a pentagon.
- Each step of solving the equation is crucial for arriving at the correct answer.
Understanding these principles will help you tackle similar problems in the future!
The formula to calculate the sum of the interior angles of a polygon is:
- Sum of interior angles = (n - 2) × 180
Where "n" is the number of sides in the polygon.
Given Information
In this case, the sum of the interior angles is given as 540 degrees.
Setting Up the Equation
We can set up the equation based on the formula:
- (n - 2) × 180 = 540
Simplifying the Equation
To find "n", we can simplify the equation:
1. Divide both sides by 180:
- n - 2 = 540 / 180
- n - 2 = 3
2. Solve for n:
- n = 3 + 2
- n = 5
Conclusion
The value of n is 5, which indicates that the polygon is a pentagon. Therefore, the correct answer is option 'C', which represents a polygon with 5 sides.
Key Points to Remember
- The sum of the interior angles can help determine the number of sides.
- A polygon with 5 sides is called a pentagon.
- Each step of solving the equation is crucial for arriving at the correct answer.
Understanding these principles will help you tackle similar problems in the future!
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If the sum of the interior angles of a regular polygon is 540othen how many sides does it have?a)6b)8c)5d)9Correct answer is option 'C'. Can you explain this answer?
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If the sum of the interior angles of a regular polygon is 540othen how many sides does it have?a)6b)8c)5d)9Correct answer is option 'C'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about If the sum of the interior angles of a regular polygon is 540othen how many sides does it have?a)6b)8c)5d)9Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of the interior angles of a regular polygon is 540othen how many sides does it have?a)6b)8c)5d)9Correct answer is option 'C'. Can you explain this answer?.
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