SOLUTION: if the measures of the four interior angles of a pentagon are 112, 102, 118, and 107, what is the measure of the fifth interior angle?

Question 337157: if the measures of the four interior angles of a pentagon are 112, 102, 118, and 107, what is the measure of the fifth interior angle?

Answer by jrfrunner(365) (Show Source): You can put this solution on YOUR website!
the sum of the interior angles of an n sided figure is (n-2)*180
This is basically the number of triangles that can be formed inside the figure.
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So a pentagon has n=5 for five sides, and the total of its interior angles =(5-2)*180=540
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the four interior angles given add up to (112+102+118+107)=439
therefore the 5th interior angle is 540-43=101
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