Regular Polygon Angles

Since the interior angles are $150^ \circ$ , the exterior angles are $180^ \circ - 150^ \circ = 30^ \circ$ , hence the polygon has $\frac {360}{30} = 12$ sides.

Thus, $\angle ADB = \frac {180 ^\circ }{12}, \angle BDC = \frac {180 ^\circ }{12}$ , and so $\angle ADC = \angle ADB + \angle BDC = \frac {180^\circ \times 2}{12} = 30 ^\circ$ .

ABCD is a cyclic quadrilateral so angleADC =180-<B=30 degree