Let's break down the problem using the following rules of circles and angles:

Given:

• $DOB$ is a diameter of the circle.
• Various angles need to be found using the provided angle values and geometric properties.

Key Properties to Consider:

1. Angle in a semicircle (Thales' Theorem): Any angle subtended by a diameter on the circumference is a right angle (i.e., $\angle ADO = 90^\circ$ or $\angle ABC = 90^\circ$).
2. Central Angle Theorem: The angle subtended by an arc at the center of a circle is twice the angle subtended at any point on the remaining part of the circle.

Let’s use this information to determine each angle.

Assigning the angles:

• $\angle ADO = 90^\circ$ (by Thales' Theorem).
• From the options given, we select the appropriate angles for the other positions using properties of circles and angle relationships:

Trying the angles:

Based on the given information (24°, 28°, 34°, 38°, 52°, 58°, 114°, 120°), let's assume the following:

1. $\angle ADO = 90^\circ$ is already established by Thales' Theorem.
2. $\angle ABC = 90^\circ$ (from Thales' theorem as well, since $DOB$ is the diameter).
3. $\angle OCA = 34^\circ$.
4. $\angle ACB = 58^\circ$ (could be a supplementary angle).
5. $\angle OBC = 38^\circ$.
6. $\angle CAB = 28^\circ$.

Let me know if you'd like to discuss further details or clarifications on any part of the solution!

---

Relative questions:

1. How is Thales' theorem applied to a circle with a diameter?
2. Can you explain how the central angle theorem affects angles in a circle?
3. What is the relationship between angles on a semicircle and the diameter?
4. How do you determine if two angles are supplementary in a circle?
5. How would the sum of angles in a triangle within a circle relate to the diameter?

Tip: Always remember that the angle subtended by a diameter of a circle is a right angle. This fact is key to solving many circle-related angle problems.