Prove that a regular polygon has 5 sides if its exterior angle is 2/3 of its interior angle

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

idk

step-by-step explanation: