By the property of a tangent drawn to a circle, the radius drawn to the tangent from the center of the circle is perpendicular to the tangent. Then the angle CAO = 90.
Then the angle BAO = CAB – BAC = 90 – 75 = 15.
Triangle AOB is isosceles, since OA and OB are circular radii, then the angle ABO = BAO = 15.
Then the angle AOB = 180 – ABO – BAO = 180 – 15 – 15 = 150.
Answer: Angle AOB is 150.
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