Question

Maria constructed a regular polygon whose interior angle is 108 degrees. Determine the number of the sides of the polygon

Answer 1

To find the number of sides of the regular polygon, we first need to use the formula for calculating the interior angle of a regular polygon:

Interior angle = (n-2) * 180 / n

Where n is the number of sides of the polygon.

Given that the interior angle of the regular polygon is 108 degrees, we can set up an equation:

108 = (n-2) * 180 / n

Multiplying both sides by n to get rid of the fraction:

108n = (n-2) * 180

Distributing the 180 on the right side:

108n = 180n - 360

Subtracting 108n from both sides:

72n = 360

Dividing both sides by 72:

n = 5

Therefore, Maria constructed a regular polygon with 5 sides.