The sum of the measures of the interior angles of a convex polygon is 2700°. How do you find the number of sides?

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Answer 1 · 2018-01-03T04:06:24

No. of sides of the given polygon is #color(red)17#

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Sum of the interior angles of a regular polygon is given by the formula,

#S = (2n- 4) * # rt. angles where

S = sum of the interior angles measured in degrees &
n = no. of sides of the polygon.

Given # color (blue)(S = 2700^0)#

#:. 2700 = (2n - 4) * 90#

#2n - 4 = 2700 / 9 = 30#

#2n = 30 + 4 = 34

#n = 34 / 2 = 17#

No. Of sides of this regular polygon is #color(red)17#