ABCD-parallelogram. What is the angle ABO. Angle OCD 30 degrees, angle AOD 75 degrees.

The angle AOD and COD are adjacent angles, the sum of which is 180, then the angle COD = 180 – 75 = 105.

In the triangle CDO, we determine the value of the angle CDO. Since the sum of the inner angles of the triangle is 180, the angle CDO = 180 – COD – OCD = 180 – 105 – 30 = 45.

Angle СDО = ABO as criss-crossing angles at the intersection of parallel straight lines ВС and АD of secant ВD, then angle ABO = 45.

Answer: The AВO angle is 45.

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