Regular polygons

The number of sides of two regular polygons differ by 1. The sum of the interior angles of the polygons is in the ratio of 3:2. Calculate the number of sides of each polygon.

Correct answer:

n1 =  4
n2 =  5

Step-by-step explanation:

n2n1=1 s2:s1 = 3:2  sn = 180(n2)  s2:s1 = 3:2  2   180(n22 ) = 3 180(n12)  2 180((n1+1)2)=3 180 (n12)  2 180 ((n1+1)2)=3 180 (n12)  180n1=720  n1=180720=4  n1=4
n2=n1+1=4+1=5   Verifying Solution:   d=n2n1=54=1  s1=180 (n12)=180 (42)=360  s2=180 (n22)=180 (52)=540   r=s2:s1=540:360=23=121=1.5=3:2

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