Answer:
36° or 101°
Step-by-step explanation:
Consider the figures given in the attachment.
Point C can be between A and B as shown in the left image of the attachment or outside AB chord as shown in the right image.
In both figures, ∠AOB = 115° and ∠AOC = 43°.
Both the triangles are isoceles triangle as OC and OA side is equal in ΔAOC and OA and OB is equal in ΔAOB.
In ΔAOC,
∠A + ∠O + ∠C = 180°
∠A = ∠C
∴ 2 ∠A =180-43=137°
∴∠A = 68.5
In ΔAOB,
∠A + ∠B + ∠O = 180°
∠A = ∠B
∴2 ∠A = 180-115=65°
∴∠A = 32.5°
For figure on the left side,
∠BAC = ∠OAC - ∠OAB = 68.5 - 32.5 =36°
For figure on right side,
∠BAC = ∠OAC + ∠OAB = 68.5 + 32.5 =101°
