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## 'Weekly Problem 15 - 2012' printed from http://nrich.maths.org/

It can possess all five properties.

The description does not say that
heptagon has to be convex, i.e. all of its interior angles need not
be less than $180^{\circ}$. Since $(2 \timesĀ 7 - 4) \times 90
= 900$, the interior angles of all heptagons total $900^{\circ}$.
The creation of a heptagon with all the given conditions is
possible as the diagram shows. Notice that four of the interior
angles are acute and the other three are reflex angles.

*This problem is taken from the UKMT Mathematical Challenges.*

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