Question

Please answer this. I want the answer quickly.

Answer 1

In triangle OCB,
=> OC = OB (radii of same circle)
Therefore, triangle OBC is isosceles
=> angle OCB = angle OBC (base angles of isosceles triangle) ...(1)
=> angle BOC = 130

=> angles BOC+OCB+OBC = 180 (sum of interior angles)
=> 2OBC+130 = 180 (From 1)
=> 2OBC = 50
=> OBC = 25

angle OBC = angle ABC = 25 (same angle)
angle OBC = angle ADC = 25
(Theorem: angles at circumferance subtended by same arc (in this case, arc AC) are equal)