Question

what is the value of x for which m || n?
○ x=40
○ x=5
○ x=105
○ x=30
(3x−15)°
105°
m
n

Explanation:

Step1: Identify Angle Relationship

For lines \( m \parallel n \), the \( 105^\circ \) angle and \( (3x - 15)^\circ \) angle are corresponding angles (or alternate interior/exterior, depending on transversal), so they should be equal. Thus, set \( 3x - 15 = 105 \).

Step2: Solve for \( x \)

Add 15 to both sides: \( 3x = 105 + 15 = 120 \).
Divide by 3: \( x = \frac{120}{3} = 40 \).

Answer:

\( x = 40 \) (corresponding to the option "x = 40")