Question

kathryn draws three pairs of intersecting lines. in each figure, she measures a pair of vertical angles. what is a reasonable conjecture for kathryn to make by recognizing a pattern and using inductive reasoning? when a pair of lines intersect, all of the angles formed are congruent. when a pair of lines intersect, the vertical angles are acute. when a pair of lines intersect, all of the angles formed are right angles. when a pair of lines intersect, the vertical angles are congruent.

Explanation:

Vertical angles are always congruent when two lines intersect. In the given figures, we see pairs of vertical - angles with equal measures (122° - 122°, 61° - 61°, 90° - 90°). This supports the conjecture that vertical angles are congruent. The other options are incorrect as not all angles formed by intersecting lines are congruent, vertical angles are not always acute, and not all angles formed by intersecting lines are right - angles.

Answer:

When a pair of lines intersect, the vertical angles are congruent.