Lines AB and CD are parallel. If 1 measures (3x + 15)°, and 4 measures 165°, what is the value of x?

Question

A.
x = 70
B.
x = -4
C.
x = 50
D.
x = 0

Answer 1

Since lines AB and CD are parallel, we can use the property of corresponding angles or alternate interior angles to find the value of \( x \).

From the problem, we have:

• One angle measures \( (3x + 15)^\circ \)
• The other angle measures \( 165^\circ \)

If these two angles are corresponding or alternate interior angles, they are equal. Thus, we can set up the equation:

\[ 3x + 15 = 165 \]

Now, let's solve for \( x \):

1. Subtract 15 from both sides: \[ 3x = 165 - 15 \] \[ 3x = 150 \]

2. Divide by 3: \[ x = \frac{150}{3} \] \[ x = 50 \]

Therefore, the value of \( x \) is \( 50 \).

The answer is \( \text{C. } x = 50 \).