anonymous
  • anonymous
The measure of an interior angle of a regular polygon is 165.6°. How many sides make up the regular polygon?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
I regular polygon has equal interior angles. And the formula for the sum of the interior angles is (n-2)180=Total Deg where n equals the number of sides. Also the sum of the exterior angles always add up to 360. Now using these 3 facts we can solve this question
anonymous
  • anonymous
1) Find the exterior angle. 2) Divide 360 by the exterior to get the number of sides
anonymous
  • anonymous
\[\frac{ (n - 2) \times 180 }{ n } = 165.6\] Solve for "n". "n" = 25

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anonymous
  • anonymous
The "n-2" is the number of triangles one can get from the polygon by drawing diagonals from one given vertex to "n-3" other vertices (all vertices except the given vertex and the 2 adjacent vertices). Example: look at a square. Take one vertex as "the vertex". You can draw only one diagonal.
anonymous
  • anonymous
All good now?
anonymous
  • anonymous
anonymous
  • anonymous
yeah i got it thanks
anonymous
  • anonymous
you're welcome

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