(1) Because AB = AC, ∠ BAC = 120, AD is the center line on the side of BC.

So ∠ b = ∠ c = 30, ∠ bad = ∠ DAC = 60.

And because BD=BE, ∠ BDE = ∠ Bed = 75.

Because ∠ bed+∠ DEA = ∠ ade+∠ EAD+∠ DEA =180.

So ∠BED=∠EAD+∠DEA is 75 = 60+∠ ade, so ∠ ade = 15.

(2) Because FM divides DC vertically, DM=CM and DMF = 90.

So △ DNF △ CMFSO ∠ FDC = ∠ C = 30, that is ∠ ADF = 60, and ∠ DAC = 60.

So ∠ DFA = 60, so △ADF is a regular triangle.

(3) Because DM=CM, the AD of CM/DC=EM/AD= 1/2 is 4.

Sin∠B=AD/AB means AD/sin∠B=AB.

AD=4, sin∠B= 1/2, so AB=8.