Answers

2015-04-02T18:54:27+08:00

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Given:
              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

Answer:

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

                 
                              
0