Question

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

Answer 1

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

Answer 2

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

Answer 3

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

"n" = 25

Answer 4

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.

Answer 5

All good now?

Answer 6

@DorelTibi ?

Answer 7

yeah i got it thanks

Answer 8

you're welcome