Yes. Property of isosceles triangle and the sum of the internal angles of a triangle.

50 + 50 + 30 + 30 + x + x = 180

x = 10

Don't know about what others think but I shall approach this problem using the property of isosceles triangles.
The two equal sides will have the same measure in angles too.
Since DA=DC, hence angle DAC must be 50. Similarly, angle ABD must be 30. Thus, angle BDA=180-60 or 120 and angle ADC=180-100=80.
Angle BDC is 120+80=200.
Also, since DB=DC, hence angle DBC= angle DCB and angle BDC=360-200=160.
160+2x=180, therefore x=10.
Hope that helps.

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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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