Please help with this GRE Quant. Comparison question (Triangle Geometry)

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My thought process was that since side AD = DC, and m and n are their opposite respective angles, then m and n must be equal to each other. My GRE practice book says that this is wrong and that the answer is D (The relationship cannot be determined from the information given). Maybe it has something to do with angle BCD = 60 degrees, but I thought that this was irrelevant because of the previous information. Can anyone explain? I have never been good with geometry. Thanks in advance.