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.
b.
c.
d.

Explanation:

To find a counter - example for the statement "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", we need to look for a case where the vertical angles are not one acute and one obtuse.

• In option A, the two lines \(l\) and \(m\) are perpendicular. When two lines are perpendicular, all four angles formed are right angles (\(90^{\circ}\)). Right angles are neither acute (\(<90^{\circ}\)) nor obtuse (\(>90^{\circ}\)).
• Option B: The two lines are not perpendicular. One pair of vertical angles is acute and the other pair is obtuse, which does not serve as a counter - example.
• Option C: Similar to option B, one pair of vertical angles is acute and the other pair is obtuse, which does not serve as a counter - example.
• Option D: The two lines are parallel. Parallel lines do not form vertical angles (vertical angles are formed by intersecting lines), so it is not a valid case for the given statement about intersecting lines forming vertical angles.

Answer:

A.