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Does any polygon have a total internal angle degree of 720? - Answers

Suppose there are N sides to this polygon. Draw a line from each corner to a point inside the polygon. That makes N triangles. The total of all the angles must be Nx180 degrees. But that includes 360 degrees around the point. Take that away and you have all the angles adding up to (N-2)x180 degrees. If you want this to be 720 (which is 180x4) then (N-2)x180 equals 4x180, so N-2=4 so N=6. So only a 6 sided polygon makes 720 degrees.



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Does any polygon have a total internal angle degree of 720? - Answers

https://math.answers.com/math-and-arithmetic/Does_any_polygon_have_a_total_internal_angle_degree_of_720

Suppose there are N sides to this polygon. Draw a line from each corner to a point inside the polygon. That makes N triangles. The total of all the angles must be Nx180 degrees. But that includes 360 degrees around the point. Take that away and you have all the angles adding up to (N-2)x180 degrees. If you want this to be 720 (which is 180x4) then (N-2)x180 equals 4x180, so N-2=4 so N=6. So only a 6 sided polygon makes 720 degrees.



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https://math.answers.com/math-and-arithmetic/Does_any_polygon_have_a_total_internal_angle_degree_of_720

Does any polygon have a total internal angle degree of 720? - Answers

Suppose there are N sides to this polygon. Draw a line from each corner to a point inside the polygon. That makes N triangles. The total of all the angles must be Nx180 degrees. But that includes 360 degrees around the point. Take that away and you have all the angles adding up to (N-2)x180 degrees. If you want this to be 720 (which is 180x4) then (N-2)x180 equals 4x180, so N-2=4 so N=6. So only a 6 sided polygon makes 720 degrees.

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      Suppose there are N sides to this polygon. Draw a line from each corner to a point inside the polygon. That makes N triangles. The total of all the angles must be Nx180 degrees. But that includes 360 degrees around the point. Take that away and you have all the angles adding up to (N-2)x180 degrees. If you want this to be 720 (which is 180x4) then (N-2)x180 equals 4x180, so N-2=4 so N=6. So only a 6 sided polygon makes 720 degrees.

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