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              Interior angle of a polygon -  144^{o}\\Find:           Number of diagonals the polygon have\\Solution:                (Let us settle with the degrees later.)       Interior angle =   [tex] \frac{180 (n-2)}{n)
         144 =  \frac{180 (n-2)}{n}
         144n = 180 n - 360
        144n - 180n = 180n - 180n - 360
         \frac{-36n = -360}{-36}
              n = 10

n = 10, that means that the polygon is a 10-sided polygon or DECAGON.
The remaining problem is its number of diagonals.
Number of diagonals =  \frac{n(n-3)}{2}
                                  =  \frac{ 10(10 - 3)}{2}
                                  =  \frac{10 (7)}{2}
                                  =  \frac{70}{2}
                                  = 35


                The regular polygon that has an interior angle of 144 degrees has 35 diagonals.

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