Note: Figure not drawn to scale.In the figure, line m is parallel to line n, and line k intersects both...

1. VISUALIZE the angle relationships in the diagram

Look carefully at where line k intersects line n:

• There's an angle marked \(x°\) on one side of the intersection
• There's an angle marked \(145°\) on the opposite side of the intersection
• These two angles are across from each other at the intersection point

What this tells us: When you have two angles on opposite sides of an intersection point, they are called vertical angles.

2. INFER which geometric property applies

Now that we've identified \(x°\) and \(145°\) as vertical angles, we need to recall what we know about them:

• Vertical angles are always congruent (they have the same measure)
• This is a fundamental property that's always true when two lines intersect

Strategic decision: We don't need to use the parallel lines information at all! The fact that m ∥ n is given, but the problem is really about the single intersection point where k crosses n.

3. Apply the vertical angles property

Since vertical angles are congruent:

\(x° = 145°\)

Therefore: x = 145

Answer: C. The value of x is equal to 145.

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak VISUALIZE skill: Students see two angles at an intersection and assume they must be supplementary (add to 180°) because they appear to be next to each other on a line.

If a student thinks x and 145 are supplementary angles (a linear pair):

• They would set up: \(x + 145 = 180\)
• Solving: \(x = 35\)

This may lead them to select Choice A (The value of x is less than 145) since 35 < 145.

Second Most Common Error:

Poor INFER reasoning: Students see that the problem mentions parallel lines and think they must use properties of parallel lines cut by a transversal (like corresponding angles, alternate interior angles, etc.).

This causes confusion because:

• They try to find relationships between angles at different intersection points
• They get distracted by the parallel lines information
• They can't identify which parallel line property to apply

This leads to confusion and guessing among the answer choices, or possibly selecting Choice D (The value of x cannot be determined) because they feel they don't have enough information.

The Bottom Line:

This problem tests whether you can correctly identify angle relationships in a diagram. The mention of parallel lines is a distractor—the solution only requires recognizing vertical angles at a single intersection point. Students who carefully VISUALIZE the specific angles marked in the diagram and correctly identify them as vertical angles will solve this quickly and confidently.