As DA = DB = DC, each of the triangle have 2 angles with the same magnitude.

Therefore,

In triangle DAC, Angle DAC = DCA = 50(the third angle is 180 -100 = 80)

In triangle BDA, Angle DAB = DBA = 30(the third angle is 180 - 60 = 120)

To determine the value of BDC,

We have a point D, and the sum of all the angles around it is 360

The third angle BDC = 360 - (80 + 120) = 160

In Triangle BDC, 160 + 2x = 180 => x = 10(Option A)

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