My name is Joan
The question is high school geometry level.
I am a teacher/parent.

The question is: How many sides does a polygon have if its smallest interior angle is 120 degrees and each sucessive angle is 5 degrees greater than the predecessor?

Thanks for your help as soon as possible!

Hi Joan,

The sum of the interior angles of a polygon with n sides is (n-2)180o. (You can find an outline of the proof in the answer to a previous question.) I then solved this problem with some arithmetic and using a table to keep track of what I was doing.

Number
of sides
(n-2) 180Sum
3180o375o
4360o510o
5540o650o
6..
7..

The first column is the number of sides in the polygon and the second column is the sum of the interior angles given by (n-2)180o. The third column is the sum of the angles in the polygon if your criteria is correct. That is for n = 3 the sum would be

120 + 125 + 130 = 375, for n = 4 the sum would be 120 + 125 + 130 + 135 = 510 and for n = 5 the sum would be 120 + 125 + 130 + 135 + 140 = 650

Continue the table until you find a row where columns two and three agree.

Cheers,
Penny
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