Question

find the angles in the question

Answer 1

Angle BDC = Angle BAC ( angle in the same segment )
So angle BDC = 60
In triangle BDC
Angle BDC +angle BCD+angle CBD = 180
40 + 60 + angle BCD = 180
angle BCD = 180 -100=80

Angle BCD + angle DAB = 180 ( sum of opposite angle of cyclic quadrilateral )
80 + angle DAC + angle BAC = 180 ( angle DAB = angle DAC + angle BAC )
80 +angle DAC +60 = 180
angle DAC = 180 -140 = 40