We know that angle subtended by arc at the center of circle is double the angle subtended at remaining part of circle.
∠AOB = 2∠ACB
∠AOB = 2 × 40° [∵ ∠ACB = 40°]
∠AOB = 80°
OA = OB (Radius of circle)
∴ ∠OAB = ∠OBA
In ΔOAB
∠OAB + ∠OBA + ∠AOB = 180°
∠OAB + ∠OAB + 90° = 180°
2∠OAB = 180° – 90°
2∠OAB = 90°
∠OAB = \(\frac { { 90 }^{ \circ } }{ 2 } \)
Thus, ∠OAB = 45°.