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Exterior angle of a regular polygon is 72. What would be the sum of its interior angles ?
- a)360
- b)480
- c)520
- d)540
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Exterior angle of a regular polygon is 72. What would be the sum of it...
The interior angle of the polygon = 180 - 72 = 108
Let there be x sides in the polygon.
108 x = (2x - 4)* 90
So, x = 5 (pentagon)
Sum of the interior angles = 5 x 108 = 540
Most Upvoted Answer
Exterior angle of a regular polygon is 72. What would be the sum of it...
Understanding Exterior Angles of Regular Polygons
To find the sum of the interior angles of a regular polygon when the exterior angle is given, you can use the following steps:
Step 1: Calculate the Number of Sides
- The formula for the exterior angle of a regular polygon is:
Exterior angle = 360° / n
where n is the number of sides.
- Given that the exterior angle is 72°, we can set up the equation:
72 = 360 / n.
- Rearranging gives:
n = 360 / 72 = 5.
Thus, the polygon is a regular pentagon with 5 sides.
Step 2: Calculate the Sum of Interior Angles
- The formula for the sum of the interior angles of a polygon is:
Sum of interior angles = (n - 2) × 180°.
- Plugging in our value of n:
Sum of interior angles = (5 - 2) × 180° = 3 × 180° = 540°.
Conclusion
- Therefore, the sum of the interior angles of a regular polygon with an exterior angle of 72° is 540°.
Final Answer
- The correct answer is option 'D' (540°).
To find the sum of the interior angles of a regular polygon when the exterior angle is given, you can use the following steps:
Step 1: Calculate the Number of Sides
- The formula for the exterior angle of a regular polygon is:
Exterior angle = 360° / n
where n is the number of sides.
- Given that the exterior angle is 72°, we can set up the equation:
72 = 360 / n.
- Rearranging gives:
n = 360 / 72 = 5.
Thus, the polygon is a regular pentagon with 5 sides.
Step 2: Calculate the Sum of Interior Angles
- The formula for the sum of the interior angles of a polygon is:
Sum of interior angles = (n - 2) × 180°.
- Plugging in our value of n:
Sum of interior angles = (5 - 2) × 180° = 3 × 180° = 540°.
Conclusion
- Therefore, the sum of the interior angles of a regular polygon with an exterior angle of 72° is 540°.
Final Answer
- The correct answer is option 'D' (540°).
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Exterior angle of a regular polygon is 72. What would be the sum of its interior angles ?a)360b)480c)520d)540Correct answer is option 'D'. Can you explain this answer?
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Exterior angle of a regular polygon is 72. What would be the sum of its interior angles ?a)360b)480c)520d)540Correct answer is option 'D'. 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 Exterior angle of a regular polygon is 72. What would be the sum of its interior angles ?a)360b)480c)520d)540Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Exterior angle of a regular polygon is 72. What would be the sum of its interior angles ?a)360b)480c)520d)540Correct answer is option 'D'. Can you explain this answer?.
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