Question

which angles are complementary to each other? select all that apply.
∠5 and ∠6
∠2 and ∠3
∠2 and ∠6
∠3 and ∠5

Explanation:

Step1: Define complementary angles

Complementary angles sum to $90^\circ$. The square indicates $\angle 4 = 90^\circ$, so the straight line gives $\angle 4 + \angle 5 + \angle 6 = 180^\circ$, meaning $\angle 5 + \angle 6 = 90^\circ$.

Step2: Use vertical angles

$\angle 2 = \angle 6$ (vertical angles), $\angle 3 = \angle 5$ (vertical angles). Substitute: $\angle 2 + \angle 3 = \angle 6 + \angle 5 = 90^\circ$, $\angle 2 + \angle 6 = \angle 6 + \angle 6$ (not $90^\circ$ unless $\angle 6=45^\circ$, no evidence), $\angle 3 + \angle 5 = \angle 5 + \angle 5$ (not $90^\circ$ unless $\angle 5=45^\circ$, no evidence).

Answer:

$\angle 5$ and $\angle 6$, $\angle 2$ and $\angle 3$