Complementary 81152

In a certain polygon, the ratio of the sum of the sizes of its internal angles and the sum of the sizes of the complementary angles is 2:5. How many vertices does this polygon have?

Correct answer:

n =  8

Step-by-step explanation:

s1:s2 = 2:5  s1 = (n2) 180   s1 = α1+α2+α3+αn s2 = (90α1)+(90α2)+(90α3)+(90αn) = 90 n  s1  s1:s2 = 2:5 5s1 = 2 s2  5 s1 = 2 (90 n  s1) 7 s1 = 2 90 n  7 (n2) 180=2 90 n  1080n=2520  n=10802520=2.33333333=8  n=372.333333  n=8   Verifying Solution:   s1=(n2) 180=(82) 180=1080  s2=n 180s1=8 1801080=360  r=s1:s2=1080:360=3=3:1



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