Question

determine the value of x that makes m || n. state the theorem or postulate that proves the lines are parallel for this value of x (1 point) if x = 5 then m || n by the consecutive interior angles converse theorem if x = 5 then m || n by the alternate interior angles converse theorem if x = 10 then m || n by the consecutive interior angles converse theorem if x = 10 then m || n by the alternate interior angles converse theorem

Explanation:

Step1: Use Consecutive Interior Angles Theorem

If \(m\parallel n\), then \((10 + 2x)+(50+10x)=180\) (Consecutive Interior Angles Theorem: if two parallel lines are cut by a transversal, then consecutive interior angles are supplementary)

Step2: Solve the equation

$$
LATEXBLOCK0
$$

Answer:

If \(x = 10\), then \(m\parallel n\) by the Consecutive Interior Angles Converse Theorem.