Question

Two lines are intersected by a third line. If ∠2 ≠ˆ ∠6, which of the following must be true about ∠2?

1) ∠2 is acute
2) ∠2 is obtuse
3) ∠2 is right
4) ∠2 is congruent to ∠6

Answer 1

If ∠2 ≠ ∠6, it means that the angles are not congruent. The measure or type of angle cannot be determined without further information.

Step-by-step explanation:

If ∠2 ≠ ∠6, it means that angle 2 is not congruent to angle 6. Since the two lines are intersected by a third line, and the angles formed by the intersections are not congruent, we can conclude that the angles are different. In this case, if ∠2 is not congruent to ∠6, it means that ∠2 and ∠6 are not equal in measure.

Therefore, none of the options 1) ∠2 is acute, 2) ∠2 is obtuse, 3) ∠2 is right, or 4) ∠2 is congruent to ∠6 can be determined solely based on the given information. We only know that the measures of these angles are not equal.