first of all assume that the values of the interior and exterior angles of the polygon are x.
Therefore interior angle is x and exterior angle is 2/3 x.
We know that the interior angle plus the exterior angle add up to 180 degrees hence
x+2/3 x=180
solve for the value of x
multiply everything by 3
3x+2x=540
add the like terms
5x=540
then simplify
x=108.
hence one interior angle is 108 degrees.
in order to find the value of one interior angle we use the formula:
(2n-4)90
--------------
n
hence:
(2n-4)90
------------- =108.
n
open the brackets:
180n-360
-------------- =108
n
multiply all sides by the denominator to eliminate it from the equation:
180n-360=108n.
collect like terms together:
180n-108n=360.
subtract 108 from 180:
180n-108n=72n.
hence 72n=360.
simplify the equation to get the value of n:
72n=360
divide both sides by 72
72n 360
---- = -----
72 72
hence n=5
