If  m∠ABF=(7b−24)° and  m∠ABE=2b°, find  m∠EBF.

To solve for \( m\angle EBF \), we need to use the information provided:

Given:
- \( m\angle ABF = (7b - 24)^\circ \)
- \( m\angle ABE = 2b^\circ \)
- \( \angle ABF \) is the entire angle made up of two parts: \( \angle ABE \) and \( \angle EBF \).

Thus, using the angle addition postulate:
\[
m\angle ABF = m\angle ABE + m\angle EBF
\]
Substitute the given values:
\[
7b - 24 = 2b + m\angle EBF
\]
Now, solve for \( m\angle EBF \):

1. Subtract \( 2b \) from both sides:
\[
7b - 24 - 2b = m\angle EBF
\]
2. Simplify the equation:
\[
5b - 24 = m\angle EBF
\]

Thus, \( m\angle EBF = 5b - 24 \) degrees.

Would you like any additional details or clarifications on this solution?

Here are some related questions to consider:
1. If \( b = 10 \), what is \( m\angle EBF \)?
2. What is the relationship between \( m\angle ABF \) and \( m\angle ABE \)?
3. How would you calculate \( b \) if \( m\angle ABF = 90^\circ \)?
4. What are the properties of angle addition in a triangle?
5. Can the equation change if \( b \) is negative?

**Tip:** Always check if the angles are supplementary, complementary, or part of a triangle for more insights into solving related problems.

Learn how to find angle EBF using the angle addition postulate with a detailed step-by-step solution. This problem involves calculating angles in a geometric context, specifically using given angle measures and properties of angles in triangles.

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