Will Angle Chasing Work?

Geometry Level 4

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

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

Then find the sum of the digits of the number \(x^{y}\).

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