2011 AIME II Problems/Problem 3

Revision as of 21:21, 30 March 2011 by Pkustar (talk | contribs)

Problem:

The degree measures of the angles in a convex 18-sided polygon form an increasing arithmetic sequence with integer values. Find the degree measure of the smallest angle.


Solution:

Set up an equation where x is the measure of the smallest angle, and y is the increase in angle measure. You get 18x+153y=2880, because (x+0y)+(x+y)+(x+2y)+...(x+17y)=18x+153y=the total angle measures of all of the angles in an 18-gon=2880 Solving the equation for integer values (or a formula that I don't know) you get x=7, and y=18 The smallest angle is therefore 7.

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