How many sides are in a polygon whose sum of the interior angles is 1440?

1 Answer
EZ as pi
Sep 10, 2016

There are 10 sides.

Explanation:

If you draw triangles inside a polygon using one vertex and joining it to all the other vertices (without line crossing) the number of triangles will be 2 less than the number of sides . Hence #(n-2)# in the formula. Each triangle has 180°.

#1440 div 180# will give the number of triangles.

Then add 2 to find the number of sides.

#1441 div 180 = 8 #triangles

#8+2 = 10 " sides"#

Or you could use the formula, it does exactly the same process.

#180(n-2) = 1440#

#n-2 = 1440/18 = 8#

#n = 8+2 = 10#

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