If  m∠ABF=(8w−6)°
and  m∠ABE=[2(w+11)]°
, find  m∠EBF
.

To find \( m\angle EBF \), we can use the fact that \( m\angle ABF \) is the sum of \( m\angle ABE \) and \( m\angle EBF \). In other words:

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

Given:
\[
m\angle ABF = (8w - 6)^\circ
\]
\[
m\angle ABE = 2(w + 11)^\circ
\]

Let's substitute these values into the equation:

\[
(8w - 6)^\circ = 2(w + 11)^\circ + m\angle EBF
\]

Now, solve for \( m\angle EBF \):

1. Expand the equation:
\[
8w - 6 = 2w + 22 + m\angle EBF
\]

2. Subtract \( 2w \) and 22 from both sides:
\[
8w - 2w - 6 - 22 = m\angle EBF
\]

3. Simplify:
\[
6w - 28 = m\angle EBF
\]

Thus, the measure of \( m\angle EBF \) is:
\[
m\angle EBF = 6w - 28
\]

Would you like more details or have any questions about this solution?

Here are 8 related questions:
1. How do you determine if two angles are supplementary?
2. What is the sum of angles in a triangle?
3. Can you find the value of \( w \) if \( m\angle EBF \) is known?
4. How do you express angles as algebraic expressions?
5. What is the difference between adjacent and vertical angles?
6. How do you use the angle addition postulate in geometry?
7. What other methods could be used to solve for \( m\angle EBF \)?
8. How would you solve for \( m\angle EBF \) if additional angles were given?

**Tip:** When dealing with angles, always check if they are complementary, supplementary, or part of a geometric shape to find relationships easily.

Discover how to find angle EBF given angle ABF and angle ABE using the Angle Addition Postulate. This detailed math solution covers geometric angles and equations. Suitable for high school students.

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