The tangent BA (tangent point A) is drawn to the circle with center O. It is known that the angle OBC = 130 degrees. Find the angle AOB
The angle ABO is adjacent to the angle OBC, the sum of which is 180, then the angle ABO = (180 – OBC) = (180 – 130) = 50.
The segment OA is the radius of the circle drawn to the point of tangency, then AO is perpendicular to the tangent AB, which means that the triangle AOB is rectangular.
The sum of the acute angles of a right-angled triangle is 90, then the angle AOB = (90 – ABO) = (90 – 50) = 40.
Answer: The AOB angle is 40.
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