Question

when two parallel lines are cut by a transversal, which of the statements is not true?
same - side interior angles are congruent.
vertical angles are always congruent.
corresponding angles are congruent.
alternate interior angles are congruent.
question 13
1 pts
for what value of x is line m parallel to line n?

Explanation:

Step1: Recall angle - relationships for parallel lines cut by a transversal

When two parallel lines are cut by a transversal, vertical angles are always congruent, corresponding angles are congruent, and alternate - interior angles are congruent. Same - side interior angles are supplementary (their sum is 180°), not congruent. So the statement "Same - side interior angles are congruent" is not true for parallel lines cut by a transversal.

Step2: For the second question, use the property of corresponding angles

If line \(m\) is parallel to line \(n\), then the corresponding angles are equal. The angle corresponding to the \(115^{\circ}\) angle and the \((3x + 5)^{\circ}\) angle must satisfy the condition for parallel lines. First, find the non - \(115^{\circ}\) angle adjacent to the \(115^{\circ}\) angle on line \(m\). Since they are a linear pair, this angle is \(180 - 115=65^{\circ}\). For lines \(m\) and \(n\) to be parallel, \(3x + 5=65\).

Step3: Solve the equation \(3x + 5 = 65\) for \(x\)

Subtract 5 from both sides of the equation: \(3x+5 - 5=65 - 5\), which gives \(3x = 60\). Then divide both sides by 3: \(x=\frac{60}{3}=20\).

Answer:

1. The statement "Same - side interior angles are congruent" is not true.
2. \(x = 20\)