Asked by brinlee
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
One-half
2
8
12
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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 \( \boxed{2} \).
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 \( \boxed{2} \).
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