To determine the number of sides of a regular polygon based on its interior angle, we can use the formula for the interior angle of a regular polygon:
Interior Angle (I) = (n – 2) * 180 / n
Where n is the number of sides. In this case, we know that each interior angle is 162 degrees. So, we can set up the equation:
162 = (n – 2) * 180 / n
To eliminate the fraction, we can multiply both sides by n:
162n = (n – 2) * 180
Now, expanding the right side:
162n = 180n – 360
Next, we can rearrange the equation to isolate n:
360 = 180n – 162n
360 = 18n
Finally, dividing both sides by 18 gives us:
n = 20
Thus, the regular polygon has 20 sides.