maths!!!!

∠BAD = 75 (共圓四邊形外角)
∠BAD : ∠ADC = arc BCD : arc ABC = 3 : 2
Therefore ∠ADC = 50
Hence ∠ABC = 130 (共圓四邊形對角)

Let centre be O
angle BAD = angle DCE = 75
(external angle of inscribed quadrilateral)
angle DOC = 2 (angle BAD) = 2 (75) = 150
(angle at centre = 2 times angle at circumference)
angle AOB = angle BOC = 0.5 angle DOC = 0.5 (150) = 75 (given)
large angle AOC = 360 - angle AOB - angle AOC
= 360 -75 - 75 = 210
angle ABC = 0.5 large angle AOC = 0.5 (210) = 105
(angle at circumference = 0.5 angle at centre)