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

it is a polygon questionhaving problem to solve it plsssssss solve it  :(

### 3 Answers by Expert Tutors

Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
1
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.

Very nice!
Thank you. The activity I used with my geometry classes a long time ago. I had read about it someplace.
thankyou so much for ur answers :D
I dont understand where you got the 156 from :/
John M. | Analytical assistance -- Writing, Math, and moreAnalytical assistance -- Writing, Math, ...
4.8 4.8 (154 lesson ratings) (154)
1
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
Kenneth G. | Experienced Tutor of Mathematics and StatisticsExperienced Tutor of Mathematics and Sta...
0
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