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