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To determine the value of \( x \) that makes line \( a \) parallel to line \( b \), we can apply the properties of corresponding or alternate interior angles for parallel lines.

### Step-by-step approach:

1. **Identify the relationships of angles**:
   - The angle marked \( (4x + 28)^\circ \) is on line \( a \).
   - The angle on line \( b \) is \( 116^\circ \), and both lines are intersected by a transversal.
   
   If the two lines \( a \) and \( b \) are parallel, then \( (4x + 28)^\circ \) and \( 116^\circ \) are corresponding angles and should be equal.

2. **Set up the equation**:
   \[
   4x + 28 = 116
   \]

3. **Solve for \( x \)**:
   \[
   4x = 116 - 28
   \]
   \[
   4x = 88
   \]
   \[
   x = \frac{88}{4} = 22
   \]

So, the value of \( x \) that makes line \( a \) parallel to line \( b \) is **22**.

Would you like more details on why corresponding angles are equal when lines are parallel?

### 5 related questions:
1. What are alternate interior angles and how do they apply to parallel lines?
2. How would the equation change if the given angle on line \( b \) were different?
3. What are other methods to determine if two lines are parallel?
4. How does the transversal line affect the relationship between angles on parallel lines?
5. What is the general rule for corresponding angles in parallel lines?

**Tip**: Always look for patterns in angle relationships when lines are cut by a transversal to identify corresponding, alternate, or consecutive interior angles.

For what value of x is line a parallel to line b? The angles given are (4x + 28)° on line a, 116° on line b, and 64° as the other angle in the figure.

This geometry problem involves finding the value of x that makes two lines parallel. Learn how to apply the corresponding angles postulate to solve for x when lines a and b are cut by a transversal.

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