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Assuming the polygon is regular with an interior angle of 172.8o then it has 50 sides.
For all polygons:
exterior_angle + interior_angle = 180o
⇒ exterior_angle = 180o - interior_angle
sum_of_exterior_angles = 360o
If the polygon is regular all angles are the same and:
sum_of_exterior_sides = number_of_sides x exterior_angle (= 360o)
⇒ number_of_sides = 360o ÷ exterior_angle
= 360o ÷ (180o - interior_angle)
Assuming your polygon is regular with each interior angle 172.8o then
number_of_sides = 360o ÷ (180o - 172.8o)
= 50 sides
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∙ 12y ago
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