Find the side of a regular polygon with a perimeter of 80 cm, if its outer corner is 4 times less than the inner one.

Let the outer angle be equal to the variable a.

Then the inner will express through 4a.

Knowing that their sum is 180 °, we write down the equation and determine the value of the internal one:

a + 4a = 180;

5a = 180;

a = 36;

4 * 36 = 144.

Let’s determine how many sides our polygon will have in this case:

144 = (n – 2) / n * 180;

144n = 180n – 360;

36n = 360;

n = 10.

Let us find out what value the length of the side of the polygon will correspond to when it is known from the condition that its perimeter is 80 cm:

80: 10 = 8.

Answer: 8 cm.