AB = AC，∠A=36，

∴∠ABC=∠ACB=72

∫G and F are the midpoint of AB and AC respectively.

∴GF∥BC and GF=BD=CD

∵GF∥BC∴∠AGF=∠ABC=∠AFG=72

AG = BG，∠AGF=∠ABC，GF=BD

∴△AGF≌△GBD∴BG=AG=AF=DG. Similarly, AF=CF=DF=GD can also be proved.

∴∠ BGD =∠ A = 36 According to the tangent angle theorem, ∠ BDH =∠ BGD = 36,

∴∠bhd= 180-∠ABC-∠bdh = 180-72-36 = 72

∴BD=HD can be proved in the same way, DE=DC.

∵DG=DF∴∠DGF=∠DFG=72

∴∠GDF=36

∫GF ∨= BC

∴ Quadrilateral GFCD is a parallelogram.

∴∠GDC=∠GFC= 108

∴∠edf=∠gdc-∠gdf-∠cde= 108-36-36 = 36 =∠dfe

∴DE=EF

∴DE=EF=GF=GH=HD=BD=DC and ∠ Def = ∠ EFG = ∠ FGH = ∠ GHD = ∠ HDE =108.

A pentagon is a regular pentagon.