SOLUTION: If the sum of all the angles except one of a convex polygon is 2190 degrees then the number of sides must be?

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Question 1122224: If the sum of all the angles except one of a convex polygon is 2190 degrees then the number of sides must be?
Answer by ikleyn(52809)   (Show Source): You can put this solution on YOUR website!
.
The sum of all interior angles of an n-sided polygon is  180°*(n-2).



The table below represents the sums of all interior angles of n-sided polygons for 3 <= n <= 16.


    Table


n     Sum of all interior angles
----------------------------------

3	180
4	360
5	540
6	720
7	900
8	1080
9	1260
10	1440
11	1620
12	1800
13	1980
14	2160
15	2340
16	2520


From the table, you easily can conclude that your polygon must have n > 14 and n <= 15 sides.   

    (It is so because the missed interior angle of a convex polygon is less than 180°).


Hence, n = 15.


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