SOLUTION: one of the interior angle of a regular polygon is 80 degrees and each of the other interior angle is 128 degrees.find the number of sides of the polygon

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Question 1132997: one of the interior angle of a regular polygon is 80 degrees and each of the other interior angle is 128 degrees.find the number of sides of the polygon
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
one of the interior angle of a regular polygon is 80 degrees and each of the other interior angle is 128 degrees.
find the number of sides of the polygon
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            Different parts of the given problem CONTRADICT each other.


            If a polygon is a regular polygon,  then  ALL  ITS  INTERIOR  ANGLES  are congruent.

            In this case,  it can not happen that one of the angles is different from other / (others).


            The condition in the post is  DEFECTIVE.



Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i believe the answer will be 6.

if the internal angle is 80, then the external angle is 180 - 80 = 100.

so one side of the polygon will have an external angle of 100 degrees.

all the other sides of the triangle will have an external angle of 180 - 128 = 52 degrees.

the sum of the external angles of a polygon is always 360 degrees.

subtract 100 from 360 and you get 260.

divide 260 by 52 and you get 5.

there are 5 sides with an external angle of 52 degrees and 1 side with an external angle of 100 degrees for a total of 6 sides.