A convex pentagon has no angles pointing inwards. More precisely, no internal angles can be more than 180°.
The figure may be labelled as shown.
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The pentagons in the figure, are ABDFH, CDFHB, EFHBD, GHBDF, ACDFG, CEFHA, EGHBC, GABDE, BDEGH, DFGAB, FHACD and HBCEF. Clearly, these are 12 in number.
