Question

select the correct answer.
prove: if two intersecting lines form two pairs of vertical angles, one pair of angles will be acute, and one pair of angles will be obtuse.
which image provides the best counterexample for this statement?
a. image of two intersecting lines l and m

b. image of two perpendicular intersecting lines l and m with a right angle symbol

c. image of two nearly parallel intersecting lines l and m

d. image of two parallel lines l and m

Explanation:

A counterexample disproves the statement. The statement claims one pair of vertical angles is acute and one is obtuse. For a counterexample, we need intersecting lines where vertical angles are not acute/obtuse (e.g., right angles).

• Option A: Intersecting lines with one acute and one obtuse pair (supports the statement, not a counterexample).
• Option B: Lines are perpendicular, so all vertical angles are right angles ($90^\circ$), neither acute nor obtuse. This disproves the statement.
• Option C: Intersecting lines with one acute and one obtuse pair (supports the statement).
• Option D: Lines are parallel (no intersection, so no vertical angles).

So Option B is the counterexample.

Answer:

B. The image with perpendicular lines (forming right angles as vertical angles)