IMO Shortlist 1981 problem 14
Dodao/la:
arhiva2. travnja 2012. Prove that a convex pentagon (a five-sided polygon)
![ABCDE](/media/m/2/7/c/27c16cf5bf2e8ca59b13c61cf1562251.png)
with equal sides and for which the interior angles satisfy the condition
![\angle A \geq \angle B \geq \angle C \geq \angle D \geq \angle E](/media/m/a/c/b/acb949080fb9b0b11207a84f403ee87c.png)
is a regular pentagon.
%V0
Prove that a convex pentagon (a five-sided polygon) $ABCDE$ with equal sides and for which the interior angles satisfy the condition $\angle A \geq \angle B \geq \angle C \geq \angle D \geq \angle E$ is a regular pentagon.
Izvor: Međunarodna matematička olimpijada, shortlist 1981