Two parallel lines are cut by a transversal. Angle 1 measures (4x + 28)°, and the angle adjacent to the alternate exterior angle with angle 1 measures (14x + 8)°. What is the value of x?
One-half
2
8
12

In this problem, two parallel lines are cut by a transversal, and we are given the measure of two angles: angle 1 and an angle adjacent to its alternate exterior angle.

### Key concepts:
- **Alternate exterior angles** are congruent when two parallel lines are cut by a transversal.
- Adjacent angles on a straight line are **supplementary**, meaning they sum to \( 180^\circ \).

### Step-by-step solution:

1. **Identify the angles:**
   - Let angle 1 be \( (4x + 28)^\circ \).
   - The angle adjacent to the alternate exterior angle of angle 1 is \( (14x + 8)^\circ \).

2. Since these two angles are **adjacent** on a straight line, they are **supplementary**, meaning their sum is \( 180^\circ \).

3. Set up the equation:
   \[
   (4x + 28)^\circ + (14x + 8)^\circ = 180^\circ
   \]

4. Combine like terms:
   \[
   (4x + 14x) + (28 + 8) = 180
   \]
   \[
   18x + 36 = 180
   \]

5. Solve for \( x \):
   \[
   18x = 180 - 36
   \]
   \[
   18x = 144
   \]
   \[
   x = \frac{144}{18} = 8
   \]

### Conclusion:
The value of \( x \) is \( 8 \).

Would you like further explanation, or do you have any other questions?

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Here are 5 related questions:
1. What are alternate interior angles and their properties?
2. How do we find the value of other angles in a transversal problem?
3. Can angles on the same side of a transversal be equal?
4. What are consecutive interior angles and their relationships?
5. How do you solve equations with angles in terms of \( x \)?

**Tip:** In geometry, supplementary angles always add up to \(180^\circ\), regardless of their specific types.

Two parallel lines are cut by a transversal. Angle 1 measures (4x + 28)°, and the angle adjacent to the alternate exterior angle with angle 1 measures (14x + 8)°. What is the value of x?

This geometry problem involves finding the value of x when two parallel lines are cut by a transversal, and angles are given in terms of x. Learn how to apply the Alternate Exterior Angle Theorem and the Supplementary Angle Theorem in this step-by-step solution. Suitable for students in Grades 8-10.

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