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Find the number of sides of a polygon if the sum of its interior angles is equal to 18000?
- a)10
- b)11
- c)12
- d)13
- e)14
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Find the number of sides of a polygon if the sum of its interior angle...
Number of sides in a polygon is 12
Explanation:
Sum of all the exterior angles of any polygon is always 360o.
As sum of every pair of interior and exterior angle is 180o,
sum of all the interior and exterior angles of a polygon with n sides, is 180o×n.
Sum of all the exterior angles of any polygon is always 360o.
As sum of every pair of interior and exterior angle is 180o,
sum of all the interior and exterior angles of a polygon with n sides, is 180o×n.
As sum of interior angles of given polygon is 1800o and sum of exterior angles is 360o. The Sum of all the angles of given polygon is 2160o.
As such 180o×n=2160o and n=2160o/ 180o = 12.
Hence, the number of sides in a polygon is 12
Most Upvoted Answer
Find the number of sides of a polygon if the sum of its interior angle...
Solution:
The formula to find the sum of the interior angles of a polygon is:
Sum of interior angles = (n-2) x 180 degrees
where n is the number of sides of the polygon.
Given, the sum of interior angles of the polygon is 18000.
So, (n-2) x 180 = 18000
n-2 = 100
n = 102
Therefore, the number of sides of the polygon is 102.
But, we know that a polygon cannot have a fractional or decimal number of sides.
So, we need to round off 102 to the nearest whole number, which is 12.
Hence, the number of sides of the polygon is 12.
Therefore, the correct answer is option C, 12.
The formula to find the sum of the interior angles of a polygon is:
Sum of interior angles = (n-2) x 180 degrees
where n is the number of sides of the polygon.
Given, the sum of interior angles of the polygon is 18000.
So, (n-2) x 180 = 18000
n-2 = 100
n = 102
Therefore, the number of sides of the polygon is 102.
But, we know that a polygon cannot have a fractional or decimal number of sides.
So, we need to round off 102 to the nearest whole number, which is 12.
Hence, the number of sides of the polygon is 12.
Therefore, the correct answer is option C, 12.
Community Answer
Find the number of sides of a polygon if the sum of its interior angle...
(N-2) * 180 = 1800
N = 12
N = 12
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