Will Angle Chasing Work?

Geometry Level 4

In the figure BDA=CDB=50,DAC=20,CAB=80\angle BDA=\angle CDB=50^\circ,\angle DAC=20^\circ ,\angle CAB=80^\circ

If BCA=x,DBC=y\angle BCA=x^\circ,\angle DBC=y^\circ

Then find the sum of the digits of the number xyx^{y}.

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