find the number of sides of a regular polygon if the sum of its interior angle is 1)1260 2)1980 3)3420
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We know that sum of interior angles of a regular polygon is (n - 2) * 180.
(1) Given sum of interior angles = 1260.
1260 = (n - 2) * 180
1260 = 180n - 360
1260 + 360 = 180n
1620/180 = n
n = 9.
Therefore the number of sides = 9.
(2) Given sum of interior angles = 1980.
1980 = (n - 2) * 180
1980 = 180n - 360
1980 + 360 = 180n
2340 = 180n
n = 2340/180
n = 13.
Therefore the number of sides = 13.
(3) Given that sum of interior angles = 3420.
3420 = (n - 2) * 180
3420 = 180n - 360
3420 + 360 = 180n
3780 = 180n
n = 3780/180
n = 21.
Therefore the number of sides = 21.
Hope this helps!
(1) Given sum of interior angles = 1260.
1260 = (n - 2) * 180
1260 = 180n - 360
1260 + 360 = 180n
1620/180 = n
n = 9.
Therefore the number of sides = 9.
(2) Given sum of interior angles = 1980.
1980 = (n - 2) * 180
1980 = 180n - 360
1980 + 360 = 180n
2340 = 180n
n = 2340/180
n = 13.
Therefore the number of sides = 13.
(3) Given that sum of interior angles = 3420.
3420 = (n - 2) * 180
3420 = 180n - 360
3420 + 360 = 180n
3780 = 180n
n = 3780/180
n = 21.
Therefore the number of sides = 21.
Hope this helps!
sumit174:
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Answered by
46
Answer:
We know that sum of interior angles of a regular polygon is (n - 2) * 180.
(1) Given sum of interior angles = 1260.
1260 = (n - 2) * 180
1260 = 180n - 360
1260 + 360 = 180n
1620/180 = n
n = 9.
Therefore the number of sides = 9.
(2) Given sum of interior angles = 1980.
1980 = (n - 2) * 180
1980 = 180n - 360
1980 + 360 = 180n
2340 = 180n
n = 2340/180
n = 13.
Therefore the number of sides = 13.
(3) Given that sum of interior angles = 3420.
3420 = (n - 2) * 180
3420 = 180n - 360
3420 + 360 = 180n
3780 = 180n
n = 3780/180
n = 21.
Therefore the number of sides = 21.
Hope this helps!
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