The question in the image asks the following:

28. In the diagram below, $O$ is the center of the circle. $BOC$ is a diameter and $\angle ADC = 37^\circ$. What is $\angle ACB$?

• A. $147^\circ$
• B. $127^\circ$
• C. $65^\circ$
• D. $85^\circ$
• E. $37^\circ$

Step-by-step Explanation:

1. Circle Properties:

   • $O$ is the center of the circle.
   • $BOC$ is a diameter, so the angle subtended by the diameter on the circumference will be a right angle ($90^\circ$).

2. Given Angles:

   • $\angle ADC = 37^\circ$.

3. Using Circle Theorems:

   • Since $BOC$ is a diameter, the angle subtended by this diameter at the circumference at point $A$, i.e., $\angle ACB$, must be $90^\circ$. This is a direct result of the "Angle in a semicircle" theorem.

4. Answer: The angle $\angle ACB$ is $90^\circ$.

However, none of the options provided in the question match $90^\circ$. This might indicate an error in the options, or the question could have additional conditions that we missed.

Would you like to verify or review this further? Feel free to ask any follow-up questions or request additional clarifications.

Follow-up Questions:

1. What other properties of a circle could help solve problems like this?
2. How do you apply the "Angle in a semicircle" theorem in other geometric shapes?
3. How does knowing the center of a circle impact angle calculations?
4. What are other common theorems related to circles and angles?
5. How would you verify your final answer using construction?

Tip:

Remember, in any problem involving a diameter of a circle, always check if you can apply the semicircle property, as it frequently simplifies angle calculations.