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?

Question

One-half
2
8
12

Answer 1

To solve the problem, we first need to identify the relationships between the angles formed by the two parallel lines and the transversal.

Given:

• Angle 1 measures \( (4x + 28)^\circ \)
• The angle adjacent to the alternate exterior angle with angle 1 measures \( (14x + 8)^\circ \).

Since angle 1 and the adjacent angle are corresponding angles created by the transversal crossing the parallel lines, they are equal. Therefore, we can set up the equation:

\[ 4x + 28 = 14x + 8 \]

Now, we will isolate \( x \):

1. Subtract \( 4x \) from both sides: \[ 28 = 10x + 8 \]

2. Subtract 8 from both sides: \[ 20 = 10x \]

3. Divide both sides by 10: \[ x = 2 \]

Thus, the value of \( x \) is \( \boxed{2} \).