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