Answer:
C) ∠7 and ∠9
Explanation:
Complementary angles are two angles whose measures sum to 90°.
Note that the two angles do not have to be adjacent to one another.
As lines a and b are parallel, and ∠2 and ∠4 are denoted as right angles, the sum of ∠6 and ∠7, and the sum of ∠9 and ∠10, are both 90° since angles on a straight line sum to 180°.
As ∠6 ≅ ∠7 and ∠9 ≅ ∠10 then angles ∠6, ∠7, ∠9 and ∠10 must each be 45°. Therefore, any two of these four angles are complementary.
- ∠6 + ∠7 = 90°
- ∠6 + ∠9 = 90°
- ∠6 + ∠10 = 90°
- ∠7 + ∠9 = 90°
- ∠7 + ∠10 = 90°
- ∠9 + ∠10 = 90°
Therefore, the pair of angles that are complementary from the given answer options is ∠7 and ∠9.