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No interior angle of a convex polygon can exceed 180 degrees. A non-convex polygon has at least one reflex angle (> 180 degrees).

Alternatively, a polygon is convex if, given any two points on or inside the polygon, the straight line joining the two points must lie wholly on or inside the polygon. In a non-convex polygon, it is possible to find a pair of points such that the straight line joining them lies outside the polygon for at least some of its length.

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Q: How do you determine whether a polygon is convex or non-convex?
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Related questions

Is triangle is a convex or nonconvex?

A triangle is normally nonconvex on a flat surface


Is the sum of interior angles of a convex polygon the same as a non convex polygon?

Yes, the angle sums will be the same regardless of whether or not it is a convex polygon.


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If, for any two points A and B in the polygon, all points with position A + kB are inside the polygon for 0 ≤ k ≤ 1, then the polygon is convex. In simple terms, if all points on the line AB lie inside the polygon, it is convex. If there is at least one point on AB that is outside the polygon then it is not a convex polygon.


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