Count the number of convex pentagons in the adjoining figure.

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Solution

The correct option is C 12
A convex pentagon has no angles pointing inwards. More precisely, no internal angles can be more than $180^{o}$ .
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
The figure may be labelled as shown.

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