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A polygon is convex if, for every pair of points P and Q belonging to the polygon, the line segment PQ lies completely inside or on the polygon. Which one of the following is NOT a convex polygon?

1. A polygon in which all interior angles are less than 180b0
2. A polygon in which at least one interior angle is greater than 180b0
3. A polygon in which every diagonal lies completely inside the polygon
4. A polygon in which the line segment joining any two points of the polygon lies completely inside or on the polygon

Correct answer: A polygon in which at least one interior angle is greater than 180b0

Solution

A polygon is convex only if all interior angles are less than 180b0 and every segment joining two points lies inside it. If at least one interior angle exceeds 180b0, the polygon is concave, so it is not convex.

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