## DorelTibi Group Title The measure of an interior angle of a regular polygon is 165.6°. How many sides make up the regular polygon? one year ago one year ago

1. ChmE Group Title

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 Group Title

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

3. tcarroll010 Group Title

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

4. tcarroll010 Group Title

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 Group Title

All good now?

6. tcarroll010 Group Title

@DorelTibi ?

7. DorelTibi Group Title

yeah i got it thanks

8. tcarroll010 Group Title

you're welcome