In a circle with center O, AC and BD are diameters. the central angle AOD is 58. Find the inscribed angle ACB

Let’s finish the triangle of the AOD.

Since in the triangle AOD, AO = DO = R, the triangle AOD is isosceles.

Then the angle OAD = ODA = (180 – 58) / 2 = 61.

The inscribed angle of ADВ is equal to the angle of ADO of the ADВ triangle.

The inscribed angle ADВ rests on the arc of the AD, as well as the inscribed angle ACВ.

Then the value of the angle ACB is equal to 61.

Answer: The ACB angle is 61.