The image shows a geometric problem involving a circle with points $A$, $B$, $C$, and $D$ on its circumference. Based on the diagram, it looks like we are dealing with a cyclic quadrilateral, where the sum of opposite angles in such a quadrilateral equals $180^\circ$.

The problem specifically asks to find the value of the angle $\angle A$ or $\angle B$ as indicated by the arc drawn within the circle.

However, to give a detailed solution, I will need to verify certain details:

• Is the problem asking to calculate one of the angles?
• Are any specific values or relations given between the angles, such as $\angle A + \angle C = 180^\circ$?

Would you like to confirm any specific parts of the problem or provide additional details? Feel free to ask for a full solution explanation.

Also, here are some related questions to consider:

1. What is a cyclic quadrilateral, and how do its properties help solve problems involving circle geometry?
2. How can the inscribed angle theorem help in this type of geometry problem?
3. What role do intersecting chords play in determining angle relations in a circle?
4. Can we use arc measures to determine the value of angles in this problem?
5. How can we apply the sum of angles in a triangle to circle geometry problems?

Tip: In cyclic quadrilaterals, opposite angles always sum up to $180^\circ$. This is a useful fact when solving problems involving circles.