Question

determine the value of x for which m || n. state the theorem or postulate that proves the lines are parallel for this value of x
if x = 10, then m || n by the consecutive interior angles converse theorem
if x = 12, then m || n by the consecutive interior angles converse theorem
if x = 12, then m || n by the alternate interior angles converse theorem
if x = 10, then m || n by the alternate interior angles converse theorem

Explanation:

Step1: Apply Consecutive Interior Angles Converse Theorem

For \(m\parallel n\), \((24 + 8x)+10x=180\) (Consecutive Interior Angles Converse: if the sum of consecutive interior angles is \(180^{\circ}\), then the lines are parallel)

Step2: Solve the equation

$$
LATEXBLOCK0
$$

Answer:

B. If \(x = 12\), then \(m\parallel n\) by the Consecutive Interior Angles Converse Theorem