Question

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?

Explanation:

Step1: Recall vertical - angle properties

Vertical angles are equal. When two lines intersect, the sum of adjacent angles is 180 degrees.

Step2: Analyze each option

• Option A: One pair of vertical angles is acute and one pair is obtuse. This does not serve as a counter - example.
• Option B: The lines are parallel, so there are no vertical angles formed by intersection. This is not relevant.
• Option C: One pair of vertical angles is acute and one pair is obtuse. This does not serve as a counter - example.
• Option D: When two lines are perpendicular, all four angles are right angles (90 degrees). There are two pairs of vertical angles, and neither pair is acute or obtuse. This is a counter - example.

Answer:

D