ABCD is an inscribed quadrilateral. AD, BC are produced to meet at X. If angle B= 80 degrees and angle X= 30 degrees, find angle XCD.

Answer 1

I will assume you mean "inscribed in a circle"
In a cyclic quadrilateral, the opposite angles are supplementary, so angle D = 100°
Also angle ADC is an exterior angle in triangle DCX, so
angle DCX + angle CXD = angle ADC
angle DCX + 30 = 100
angle DCX = 70°

Answer 2

30

Answer 3

50 degrees