What information do we know and how do we use it to model this situation?
color(green)("Let the number of sides be "n)Let the number of sides be n
color(green)("Let internal angle be "color(white)(.......)A_i
color(green)("Let external angle be "color(white)(.......)A_e
Assumption: External angle less than internal angle color(green)(-> A_e < A_i)
Thus color(green)(A_i - A_e>0 => A_i - A_e=100
Not that sum " is: the sum of"
color(brown)("Known: "underline("Sum of internal angles is")color(white)(..)color(green)((n-2)180))
So color(green)(sumA_i = (n-2)180................................(1))
color(brown)("Known:"underline(" Sum of external angles is")color(white)(..)color(green)(360^0))
So color(green)(sumA_e=360 ..............................................(2))
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color(blue)("Equation (1) - Equation (2)")
sum (A_i-Ae)= (n-2)180 -360
But also sum (A_i-Ae)= sum "difference"
There are n sides each with a difference of 100^0
So sum "difference" = 100n giving:
color(green)(sum (A_i-Ae) = 100n = (n-2)180 -360.................(3))
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color(blue)("Collecting like terms")
100n = 180n - 360 - 360
80n =720
n=720/80 = 9
