DorelTibi 2 years ago The measure of an interior angle of a regular polygon is 165.6°. How many sides make up the regular polygon?

1. ChmE

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

2. ChmE

1) Find the exterior angle. 2) Divide 360 by the exterior to get the number of sides

3. tcarroll010

$\frac{ (n - 2) \times 180 }{ n } = 165.6$ Solve for "n". "n" = 25

4. tcarroll010

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.

5. tcarroll010

All good now?

6. tcarroll010

@DorelTibi ?

7. DorelTibi

yeah i got it thanks

8. tcarroll010

you're welcome