Question
Lines AB and CD are parallel. If 1 measures (2x + 12)°, and 4 measures 100°, what is the value of x?
A.
x = 34
B.
x = 44
C.
x = -4
D.
x = 136
Answers
GPT-4o mini
Since lines AB and CD are parallel, we can use the properties of corresponding angles, alternate interior angles, or same side interior angles.
1. From the information given, let’s assume that angle 1, which measures \((2x + 12)^\circ\) is corresponding to one of the given angles (angle 4 that measures \(100^\circ\)).
2. According to the property of corresponding angles, we have:
\[
2x + 12 = 100
\]
3. Now, let's solve for \(x\):
\[
2x + 12 - 12 = 100 - 12 \\
2x = 88 \\
x = \frac{88}{2} \\
x = 44
\]
So, the value of \(x\) is \(44\).
Therefore, the correct answer is **B. x = 44**.
1. From the information given, let’s assume that angle 1, which measures \((2x + 12)^\circ\) is corresponding to one of the given angles (angle 4 that measures \(100^\circ\)).
2. According to the property of corresponding angles, we have:
\[
2x + 12 = 100
\]
3. Now, let's solve for \(x\):
\[
2x + 12 - 12 = 100 - 12 \\
2x = 88 \\
x = \frac{88}{2} \\
x = 44
\]
So, the value of \(x\) is \(44\).
Therefore, the correct answer is **B. x = 44**.