Calculate the angle AOC in the given diagram.

Analysis:

• The image shows a circle with center O and points A, B, C on the circumference.
• Angle ABC is given as 40 degrees.
• We need to find angle AOC.

Angle AOC is the central angle subtended by the arc AC.

Angle ABC is the inscribed angle subtended by the same arc AC.

The relationship between a central angle and an inscribed angle that subtend the same arc is that the central angle is twice the inscribed angle.

Therefore, ∠AOC = 2 * ∠ABC.

∠AOC = 2 * 40° = 80°.

Ответ: 80°