3. Adjacent angles are ones that share a side. Complementary angles are ones that sum to 90°. This question asks you to find angles that share a side and sum to 90°. You do this by looking for a 90° angle that is divided into two or more parts.
The only 90° angles in the figures are ∠KJL and ∠LJN. The first of these has no divisions, but ∠LJN is divided by segment MJ. Hence the two angles you're looking for are
... ∠MJL and ∠MJN
4. This is the same idea as for problem 3, but the sum of the angles is a straight line. The line KN is the only one in the figure that has segments intersecting it so as to create supplementary angles. A suitable pair of supplementary angles could be any of the three pairs ...
- ∠LJK, ∠LJN
- ∠MJK, ∠MJN
- ∠PJK, ∠PJN
5. Here, you're looking for two angles that sum to 90°, but do not share a side. There are only single copies of each of the acute angles, so we know that neither the 34° angle nor the 56° angle will be part of the solution. That only leaves the 41° and 49° angles, which (happily) sum to 90°. The angles you're looking for are ...
... ∠EGF and ∠NJP
6. This is asking for two angles that sum to 180°, but do not share a side. This suggests you're looking for an angle in each figure that can be summed with an angle in the other figure. The 41° angle in the left figure would need to be paired with one of 139° (there aren't any). The 124° angle in the left figure needs to be paired with a 56° angle, which does exist.
The angles you're looking for are ...
... ∠FGH and ∠LJM
