The given question is asking to find the value of angle ∠BOC in the diagram.

Steps to solve:

1. The lines $AB$, $CD$, and $EF$ intersect at point $O$.
2. You are given two angles: ∠AOF = 98° and ∠DOE = 54°.
3. Since the angles around point $O$ form a complete circle, the total sum of all angles is 360°.

Now, using this information:

• ∠AOF + ∠BOC + ∠DOE = 180° (because these are supplementary angles on a straight line).

Let's calculate:

• ∠BOC = 180° - (∠AOF + ∠DOE)
• ∠BOC = 180° - (98° + 54°)
• ∠BOC = 180° - 152°
• ∠BOC = 28°

So, ∠BOC is 28°.

Would you like further details or have any questions? Here are five related questions for you:

1. How do we find angles around a point?
2. What is the concept of supplementary angles?
3. How can you verify the sum of angles in a circle?
4. What would change if one of the angles was given differently?
5. How do we classify angles (acute, obtuse, etc.) based on their measurement?

Tip: Always remember that the sum of angles around a point is 360°, which helps in solving many geometry problems.