https://file.aiquickdraw.com/mathbot/file/1728519834218ca1vj17n.jpg

This is an image showing a pair of parallel lines, and we are given two angles: one is \(107^\circ\) and the other is expressed as \((4x + 11)^\circ\). These two angles are corresponding angles because they are formed by a transversal cutting across parallel lines. 

Corresponding angles are congruent (equal), so we can set up the equation:
\[
4x + 11 = 107
\]

### Now, let's solve for \(x\):

1. Subtract 11 from both sides:
\[
4x = 107 - 11
\]
\[
4x = 96
\]

2. Divide both sides by 4:
\[
x = \frac{96}{4}
\]
\[
x = 24
\]

So, the value of \(x\) is \(24\).

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

Here are some related questions you might find helpful:
1. How can we prove that the lines in this image are parallel?
2. What are alternate interior angles, and how are they related to this problem?
3. How would the solution change if the lines were not parallel?
4. What is the definition of corresponding angles?
5. How can you use this concept of corresponding angles in real-life situations?

**Tip**: Whenever two lines are parallel and cut by a transversal, corresponding angles are always equal.

Find the value of x given two corresponding angles: 107° and (4x + 11)°.

Learn how to solve for x by using the concept of corresponding angles with parallel lines. This problem involves setting up a linear equation with the given angles 107° and (4x + 11)° and solving for x. Suitable for students in Grades 8-10.

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