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1. calculate the number of sides of a regular polygon whose interior angles are each 156 degree.

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3 Answers

The number of degrees in each angle of a regular polygon with n sides is 180(n-2)/n .
 
180(n-2)/n = 156,  180(n-2) = 156n,  
 
So 24n = 360,  n = 360/24  = 15 sides
 
 
The sum of the exterior angles of a polygon is 360°. (Make believe a [big] polygon is traced on the floor. Stand on one of the vertices and face in direction of one of the sides from that vertex. Walk along all sides of polygon until you're back to the starting point. How many rotations did you do? One! = 360°)
 
For regular polygons the exterior angles are the same (congruent).
 
Interior + exterior = 180°
 
156° + exterior = 180°
 
exterior = 24°
 
360°/24° = 60/4 = 30/2 = 15 sides.

Comments

Thank you. The activity I used with my geometry classes a long time ago. I had read about it someplace.

Comment

If n=# of sides of a regular polygon, then the sum of the interior angles of the polygon is equal to both
(n-2)180 and 156n
setting these two values equal gives
180n - 360 = 156n
24n = 360
n = 15