FC = FE (manufacturing)

∴∠ FEC =∠ FCE = 24 (equilateral and angular)

∠∠ Dirk +∠ EDC+∠ DCE = 180 (triangle interior angle and 180)

∠∠EDC =∠DCE = 24 (known)

∴∠DEC= 132

∴∠DEF=∠DEC-∠FEC= 108

∠∠ADE =∠ADC-∠EDC = 96-24 = 72

∠∠DEF =∠DAE+∠ADE (the nature of triangle outer angle)

∴∠DAE=36

∠∠EAB =∠ Bad -∠DAE=96 -36 =60

∠∠ade+∠DEA+∠DAE = 180 (triangle interior angle sum 180)

∴∠DEA=∠ADE=72

∴AD=AE (equilateral)

AD = AB (known)

∴AB=AE (equivalent substitution)

∴△ABE is an equilateral triangle (an isosceles triangle with an internal angle of 60 is an equilateral triangle).