Hehe, you used the wrong method. Use this to extend GF, pass through C as CM//AG, pass through the extension line of GF at M, and connect DM.

AC//GF, which is AC // GM.

∴ Quadrilateral ACMG is a parallelogram.

∴ag=ad=dc=cm,∠aed=∠dfm= 120

∫∠ADE = 15

∴∠DAG=30，∠GAE=∠CMF=75，∠ACM= 105

∴∠ DCM = 60 so △DCM is an equilateral triangle.

∴DM=AD,∠DMF=∠ADE= 15

∴△AED is equal to△△△ DFM.

∴FM=ED,AE=DF

AC = GM

That is BD=GF+FM=DF+ ED.

And at RT△GDF, ∠ GFD = 60.

∴∠DGF=30

∴GF=2DF

∴ BD=2DF+ED