how many sides does a regular polygon have if each interior angle is 144

Question

anonymous · Answer

Break up the polygon in your head. Maybe draw a picture of the polygon as a bunch of isosceles triangles that intersect at the center of the circle. 

If n stands for the number of sides on the polygon, the angle that goes out from the center is 360/n. That means that the other two angles added together are the angle of the polygon. And since they make up the angle of a triangle, they add to 180 degrees. 

So 120+360/n=180 
360/n=180-120=60 
60*n=360 
n=360/60=6 
hexagon 

So 140+360/n=180 
360/n=180-140=40 
40*n=360 
n=360/40=9 
nonagon 

So 144+360/n=180 
360/n=180-144=36 
36*n=360 
n=360/36=10 
decagon

anonymous · Answer

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