Diagram illustrating angles formed by intersecting rays at point B on a straight line.

To solve the problem, we need to analyze the given geometric configuration and use properties of angles formed by intersecting lines. Let's break it down step by step.

Step 1: Identify the given information

- We have a straight line \( AC \) with point \( B \) on it.
- Lines \( BE \) and \( BF \) intersect at point \( B \).
- Line \( BD \) is another line that intersects \( AC \) at point \( B \).

Step 2: Understand the relationships between the angles

- Since \( AC \) is a straight line, the angles on a straight line sum up to \( 180^\circ \).
- The angles around point \( B \) form a full circle, so the sum of all angles around \( B \) is \( 360^\circ \).

Step 3: Use the properties of vertical angles

- Vertical angles are the angles opposite each other when two lines intersect. They are always equal.
- For example, if \( \angle ABE \) and \( \angle DBF \) are vertical angles, then \( \angle ABE = \angle DBF \).
- Similarly, if \( \angle EBD \) and \( \angle FBC \) are vertical angles, then \( \angle EBD = \angle FBC \).

Step 4: Use the properties of supplementary angles

- Angles that form a linear pair (i.e., angles on a straight line) are supplementary. This means their measures add up to \( 180^\circ \).
- For example, \( \angle ABE + \angle EBC = 180^\circ \).
- Similarly, \( \angle DBF + \angle FBC = 180^\circ \).

Step 5: Solve for the specific angles

Without specific angle measures provided in the image, we can only describe the relationships. However, if we assume some specific angles are given, we can use the above properties to find the unknown angles.

For example, if we are given:
- \( \angle ABE = 50^\circ \)
- \( \angle DBF = 50^\circ \) (since they are vertical angles)
- \( \angle EBD = 70^\circ \)
- \( \angle FBC = 70^\circ \) (since they are vertical angles)

We can verify:
- \( \angle ABE + \angle EBC = 180^\circ \)
- \( 50^\circ + \angle EBC = 180^\circ \)
- \( \angle EBC = 130^\circ \)

Similarly, we can find other angles using the same principles.

Final Answer

Since the problem does not provide specific angle measures, the solution is based on the relationships described. If specific angles were given, we could calculate them using the above properties.

The general solution is:
\[
\boxed{\text{Vertical angles are equal, and angles forming a linear pair are supplementary.}}
\]