Adventitious Quadrangle

1. $\angle ADC = \angle ACD = 70^{\circ} \implies AC = AD$

2. Construct a circle centered at $A$ and passes through $C$ and $D$ .

3. $\angle CAD = 40^{\circ} , \angle CBD = 20^{\circ} \implies B$ is on the circle. (Inscribed angle theorem)

4. $\angle BAC = 2\angle BDC = 80^{\circ}$ (Inscribed angle theorem)

$\therefore x = 80^{\circ}$