SOLUTION: Each exterior angle is 100� less than its interior angle of a regular polygon. Find the number of sides of the polygon. Thank you!

Question 785529: Each exterior angle is 100� less than its interior angle of a regular polygon. Find the number of sides of the polygon.
Thank you!
Found 2 solutions by KMST, MathTherapy:
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The exterior and interior angles of a polygon are supplementary *adding to 180^o}}}.
If = measure of an interior angle in degrees.
= measure of the corresponding exterior angle in degrees.
The problem says that
, so

and the exterior angles measure
The exterior angles are the angles you have to turn (deviate from your original direction when going around the polygon, so they add to , because going one full turn around you are doing a .
This is a regular polygon, so it is very symmetrical:
all the exterior angles measure the same ,
all the interior angles measure the same , and
all the sides have the same length, which we do not know and do not care.
So if = number of sides/exterior angles of the regular polygon, and all those exterior angles measure
so
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Answer by MathTherapy(10551) (Show Source): You can put this solution on YOUR website!

Each exterior angle is 100� less than its interior angle of a regular polygon. Find the number of sides of the polygon.
Thank you!

Let measure of each exterior angle be E
Then measure of each interior angle = E + 100

Since both angles are supplementary, then: E + E + 100 = 180

2E = 180 - 100

2E = 80

E, or measure of each exterior angle = , or

Since the sum of the measures of the exterior angles of ALL polygons is , and with each exterior angle of this REGULAR polygon being , then the number of sides of this polygon = , or
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