Angles in a polygon

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)180^o. (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) 180	Sum
3	180^o	375^o
4	360^o	510^o
5	540^o	650^o
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)180^o. 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 Go to Math Central