Convex and Concave Polygons

In the adjoining figure of a parallelogram there are four interior angles i.e., ∠BAD, ∠ADC, ∠DCB and ∠CBA. None of the four interior angles is greater than equal to 180° and no portion of the diagonals lies in the exterior.

In the adjoining figure of a rectangle there are four interior angles i.e., ∠CBA, ∠DCB, ∠ADC and ∠BAD. None of the four interior angles is greater than equal to 180°.

In the adjoining figure of a pentagon there are five interior angles i.e., ∠ABC, ∠BCD, ∠CDE, ∠DEA and ∠EAB. None of the five interior angles is greater than equal to 180°.

In the adjoining figure of a triangle there are three interior angles i.e., ∠ABC, ∠BCA, and ∠CAB. None of the three interior angles is greater than equal to 180°.

In the adjoining figure of a hexagon there are six interior angles i.e., ∠ABC, ∠BCD, ∠CDE, ∠DEF, ∠EFA and ∠FAB.  Among the six interior angles, ∠CDE is greater than 180°.

In the adjoining figure of a septagon there are seven interior angles i.e., ∠ABC, ∠BCD, ∠CDE, ∠DEF, ∠EFG, ∠FGA and ∠GAB.  Among the seven interior angles, ∠DEF is greater than 180°.

In the adjoining figure of a quadrilateral there are four interior angles i.e., ∠ABC, ∠BCD, ∠CDA and ∠DAB.  Among the four interior angles, ∠BCD is greater than 180°.