Question

ABCD is a cyclic quadrilateral.∠ABC=130 then∠ADC

Answer 1

If AB is parallel to DC, then AD and BC are equal length. The total angle is 360, if you subtract DAB and CBA (each two times CAB), you have 240 remaining. So ADC=DCB=120 degrees.

Answer 2

angle ABC + angle ADC= 180 degree ( opp sides of a cyclic quadrilateral are supplementary)
130 + angle ADC=180 degree
angle ADC=50