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find angle in a two (a) squares (b) regular pentagons formation

Source: Sharygin Geometry Olympiad 2006 Correspodence Round (CR) 4 VIII a , IX b

August 22, 2019
geometryRegularpentagonSquares

Problem Statement

a) Given two squares ABCDABCD and DEFGDEFG, with point EE lying on the segment CDCD, and pointsF,G F,G outside the square ABCDABCD. Find the angle between lines AEAE and BFBF. b) Two regular pentagons OKLMNOKLMN and OPRSTOPRST are given, and the point PP lies on the segment ONON, and the points R,S,TR, S, T are outside the pentagon OKLMNOKLMN. Find the angle between straight lines KPKP and MSMS.
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