Problem:
An interior angle is missing in a convex polygon that has n sides, the sum of the other interior angles is 2570
find the value of n (how many sides this polygon has).
Solution:
The polygon interior angles theorem:
The sum of the measures of the interior angles: (n-2)*180
Let x=the measure of the missing interior angle
(n-2)*180=2570+x
x=180n-2930
Since this is a convex polygon
0<x<180
therefore:
0<180n-2930<180
2930<180n<3110
16.2777<n<17.27777
Since n has to be a natural number
n has to be equal to 17
Therefore n=17
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