Proposition: Prop. 13.07: Equilateral Pentagon is Equiangular if Three Angles are Equal
(Proposition 7 from Book 13 of Euclid's “Elements”)
If three angles, either consecutive or not consecutive, of an equilateral pentagon are equal then the pentagon will be equiangular.
 For let three angles of the equilateral pentagon $ABCDE$  first of all, the consecutive (angles) at $A$, $B$, and $C$  be equal to one another.
 I say that pentagon $ABCDE$ is equiangular.
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References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016