Answer:
∠ACB = 72
Step-by-step explanation:
OAD is straight line.
∠DAB + ∠OAB = 180
142 + ∠OAB = 180
∠OAB = 180 - 142
∠OAB = 38
ΔAOB is isosceles triangle. OA = OB = radius
∠OAB = ∠OBA = 38 {angles opposite to equal sides or equal}
In ΔAOB ,
∠OAB + ∠OBA + ∠AOB = 180 {Anlge sum property of triangle}
38 + 38 + ∠AOB = 180
76 + ∠AOB = 180
∠AOB = 180 - 76
∠AOB = 104
THe angle subtended by an arc of a circle at the center is double the angle subtended by it at any point on the remaining part of the circle
∠AOB = 2*∠ACB
∠ACB = ∠AOB/2
= 104/2
∠ACB = 72
