Samantha decides to increase the number of sides of a convex polygon so that the sum of its interior angle measures is increased by 720°. How many sides did Samantha add to the polygon?

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Answer 1 · 2017-12-31T20:53:11

#720 div 180 = 4# sides must be added.

Every time another side is added to a polygon the sum of the interior angles increases by #180°#

Consider the following:

#3# sides #" "rarr 180°# is the sum of the interior angles.

#4# sides #" "rarr 360°# is the sum of the interior angles.

#5# sides #" "rarr 540°# is the sum of the interior angles.

and so on...

So if the sum of the interior angles is to increase by #720°#, the number of extra sides is:

#720 div 180 = 4# sides must be added