To determine the type of polygon with an interior angle measuring 108 degrees, we can use the formula for calculating the interior angle of a regular polygon. The formula for the interior angle of a regular polygon with n sides is:
Interior Angle = (n – 2) * 180° / n
To solve for n, we can set the formula equal to 108 degrees:
108 = (n – 2) * 180 / n
Now, let’s manipulate this equation. We can multiply both sides by n to eliminate the fraction:
108n = (n – 2) * 180
Next, we distribute 180 on the right side:
108n = 180n – 360
Now, let’s move the terms involving n to one side of the equation:
360 = 180n – 108n
This simplifies to:
360 = 72n
Now we solve for n:
n = 360 / 72 = 5
This means a regular polygon with an interior angle of 108 degrees has 5 sides. Therefore, the polygon is a regular pentagon, which is characterized by having equal angles and equal side lengths.
In conclusion, if you encounter a regular polygon with each interior angle measuring 108 degrees, you can confidently say it is a regular pentagon.