Since B, D and C are points on the circle and O is the centre of the circle,

BDC
= 0.5 BOC
= 0.5 x 74
= 37 deg

because the angle at centre is twice the angle at circumference.

Since A, B, C and D are four points on the circle, they form a cyclic quadrilateral ABCD, where angle B is opposite of angle D.

The properties of such opposite angles in a cyclic quadrilateral are such that their sum is 180 deg (or in other words, the angles are supplementary). Such angle pairs are also called angles in opposite segments.

ADC
= 58 + 37
= 95 deg

So, ABC
= 180 - ADC
= 180 - 95
= 85

(angles in opposite segments are spplementary).