SOLUTION: three angles of a polygon are each 105.5,the sum of the angles in the polygon is 2520.find each of the other angles if they are equal to each other.

Algebra ->  Polygons -> SOLUTION: three angles of a polygon are each 105.5,the sum of the angles in the polygon is 2520.find each of the other angles if they are equal to each other.      Log On


   

Question 557778: three angles of a polygon are each 105.5,the sum of the angles in the polygon is 2520.find each of the other angles if they are equal to each other.
Answer by KMST(5328) About Me  (Show Source):
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For a polygon with n sides and n angles, the sum of the measures of all the interior angles equals (n-2)180 degrees.
For a polygon whose angles add up to 2520 degrees,
%28n-2%29180=2520 --> n-2=2520%2F180 --> n-2=14 --> n=16
We know the measure of 3 of the 16 angles. We have to find the measure of
16-3=13 angles.
If 3 of the angles measured 105.5 degrees, and the 13 remaining angles measure x degrees,
13x%2B3%2A105.5=2520 --> 13x%2B316.5=2520 --> 13x=2520-316.5 --> 13x=2203.5 --> x=2203.5%2F13 --> x=169.5
The 13 remaining angles measure 169.5 degrees.