Polygons

[djprinz]

Hi...

I want to know how to solve the following matter.

1) How to calculate the number of sides of a regular polygon whose interior angles are each 156°

If you can show me this with the theory, it'll help me to solve the other problems given by my math's Sir.

Thanks,
Stephanie
Sutherland International College,
Sri Lanka.

 

[Aladdin]

Each interior angle=156

Exterior angle=180-156=24 degree of each angle

the sum of the exterior angles is 360

The number of sides,n,is given by nx24 =360

n=360/24=15

The polygon has 15 sides

 

[fasteddie65]

Another, but more complicated way, is to use (n - 2)180/n = 156.
180n - 360 = 156n
24n = 360
n = 15

 

[djprinz]

I appreciate both of your help.