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The given problem is:

- \( m \angle ABF = 8s - 6 \)
- \( m \angle ABE = 2(s + 11) \)
  
We are tasked with finding \( m \angle EBF \).

Assuming that \( \angle ABE + \angle EBF = \angle ABF \), we can set up the equation:

\[
m \angle ABE + m \angle EBF = m \angle ABF
\]

Substitute the given expressions for \( m \angle ABF \) and \( m \angle ABE \):

\[
2(s + 11) + m \angle EBF = 8s - 6
\]

Let's solve for \( m \angle EBF \).

1. Expand the term \( 2(s + 11) \):
   \[
   2s + 22 + m \angle EBF = 8s - 6
   \]

2. Move \( 2s + 22 \) to the right-hand side:
   \[
   m \angle EBF = (8s - 6) - (2s + 22)
   \]

3. Simplify the right-hand side:
   \[
   m \angle EBF = 8s - 6 - 2s - 22
   \]
   \[
   m \angle EBF = 6s - 28
   \]

Thus, the measure of \( \angle EBF \) is \( 6s - 28 \).

Would you like further clarification or details on this solution?

Here are 5 related questions for further practice:
1. If \( s = 4 \), what is \( m \angle EBF \)?
2. How would the equation change if \( m \angle ABE \) was doubled?
3. What type of angle relationship is being used in this problem?
4. If \( m \angle ABF = 100^\circ \) and \( m \angle ABE = 50^\circ \), what is \( m \angle EBF \)?
5. How can you determine if \( \angle EBF \) is an acute, right, or obtuse angle?

**Tip:** When solving for unknown angles in geometry, remember that adjacent angles on a straight line or around a point often add up to a specific value (like 180° or 360°), which can help in setting up equations.

If m ∠ABF = 8s - 6 and m ∠ABE = 2(s + 11), find m ∠EBF.

Learn how to solve for the unknown angle in a geometry problem involving algebraic expressions. The solution involves using the angle addition formula and simplifying algebraic expressions. Suitable for high school students.

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