Questions on Geometry: Polygons answered by real tutors!

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Question 143400This question is from textbook CPM
: how many sides does a polygon have if the sum of its interior angles is 1440 degressThis question is from textbook CPM
: how many sides does a polygon have if the sum of its interior angles is 1440 degress
Answer by Earlsdon(3748) About Me  (Show Source):
You can put this solution on YOUR website!
You haven't indicated whether or not this is a REGULAR polygon (one whose sides are all of equal length) but I'll assume that it is.
You can start with the formula for the sum of the interior angles (S) of a regular polygon of n-sides:
S = (n-2)180 Since you know that this sum is 1440 degrees, you can substitute this into the formula and solve for n, the number of sides.
1440 = (n-2)180 Divide both sides by 180
8 = n-2 Add 2 to both sides.
n = 10
The regular polygon has 10 sides. This is known as a decagon.