Each exterior angle of a regular polygon measures 20. How many sides does the polygon have?

18 sides

The exterior angle of a polygon is the angle outside the interiour angle with the same base. For eg. Consider the following pentagon

Since the interior angle and exterior angle combined form a straight line, we can say: Interior angle + exterior angle = 180 degrees

Facts you must know: 1. All angles of a regular polygon are equal. 2. exterior angle + corresponding interior angle = 180 degrees 3. for a given polygon with sides ##n##, the total sum of interior angles = ##(n-2)xx180## 4. for a given polygon, value of one interior angle = ##"sum of interior angles"/ n##

We are given, the exterior angle is 20 degrees From 2, 20 + interior angle = 180 or, interior angle ##= 180 - 20 = 160##

Now, From 3 and 4, we can say, (assuming sides of the polygon to be n)

Value of interior angle = ##((n-2)xx180)/n## or, ##160 = ((n-2)xx180)/n## or, ##160n = 180n - 360## or, ##180n - 160n = 360## or, ##20n = 360## or, ##n=360/20## or, ##n=18##

Therefore, the polygon has 18 sides