Question 1090543: Find the measure of an interior angle and an exterior angle of a regular decagon.
Found 3 solutions by KMST, ikleyn, MathTherapy:
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! I find the exterior angles to be easier to figure out.
An exterior angle is the change in direction at a vertex as you go around the polygon.
The sum of all the exterior angles is  ,
a whole turn around the polygon, off course.
For regular polygons, the angle is the same at each vertex.
For a regular dodecagon, with  vertices, each exterior angle measures
 , off course.
Each interior angle is supplementary to an adjacent exterior angle,
so in this case, each interior angle would measure
 .
Just in case your teacher wants to see formulas,
the reasoning above would give you
 for the measure of the exterior angle of an n-hon (a polygon with n sides), and  for the measure of each interior angle.
That last formula can also be thought as coming from the fact that all the interior angles add up to the angles of the  triangles you can make by connecting one vertex (choose any) to the other vertices with straight lines.
Answer by ikleyn(52837)  (Show Source):
You can put this solution on YOUR website! .
Decagon is a a plane figure (polygon) with 10 (ten) straight sides and angles.
The exterior angle of a regular decagon is  = 36°.
The interior angle of the regular decagon is 180° - 36° = 144°.
Solved.
Answer by MathTherapy(10555)  (Show Source):
You can put this solution on YOUR website! Find the measure of an interior angle and an exterior angle of a regular decagon.
A decagon has 10 sides and angles.
A REGULAR decagon has 10 CONGRUENT sides and angles.
One of its CONGRUENT exterior angles: 
One of its CONGRUENT interior angles: 
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