SOLUTION: each interior of a regular polygon is 174 degrees what is each exterior angle? how many sides does the polygon have?

Algebra ->  Algebra  -> Polygons -> SOLUTION: each interior of a regular polygon is 174 degrees what is each exterior angle? how many sides does the polygon have?      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 238770: each interior of a regular polygon is 174 degrees what is each exterior angle?
how many sides does the polygon have?
Found 2 solutions by Earlsdon, JimboP1977:
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
The measure of each interior angle A%5Bi%5D of a regular polygon of n sides can be expressed by:
A%5Bi%5D+=+%28n-2%29%2A180%2Fn
In this problem, A%5Bi%5D+=+174degrees, so we substitute...
174+=+%28n-2%29%2A180%2Fn Multiply both sides by n and simplify.
174n+=+180n-360 Add 360 to both sides.
174n%2B360+=+180n Subtract 174n from both sides.
360+=+6n Finally, divide both sides by 6.
60+=+n
The polygon has 60 sides.
The exterior angle A%5Be%5D is supplement of the interior angle, so...
A%5Be%5D+=+180-A%5Bi%5D
A%5Be%5D+=+180-174
A%5Be%5D+=+6degrees.

Answer by JimboP1977(308) About Me  (Show Source):
You can put this solution on YOUR website!
Well a triangle has interior angles totalling 180
a square has interior angles totalling 360
a pentagon (5 sided) has interior angles totalling 540
a hexagon (6 sided) has interior angles totalling 720
so in general a n sided shape has interior angles totalling (n-2)*180. If it is regular n sided shape then each interior angle = (180*(n-2))/n
174 = (180(n-2))/n
174n = 180n-360
174n-180n = -360
-6n=-360
n = 60
180 - 174 = 6 degrees which is the exterior angle