Question

which angles are complementary to $angle2$? select all that apply.
$angle3$
$angle4$
$angle5$
$angle1$

Explanation:

Step1: Define complementary angles

Complementary angles sum to $90^\circ$.

Step2: Use right angle property

$\angle 1 = 90^\circ$, so $\angle 2 + \angle 3 = 90^\circ$ (they form a right angle together). Thus $\angle 3$ is complementary to $\angle 2$.

Step3: Use vertical/linear pair rules

$\angle 3 = \angle 5$ (vertical angles are equal). Since $\angle 2 + \angle 3 = 90^\circ$, substitute to get $\angle 2 + \angle 5 = 90^\circ$. Thus $\angle 5$ is complementary to $\angle 2$.

Step4: Eliminate other options

$\angle 1 = 90^\circ$, so $\angle 2 + \angle 1 > 90^\circ$. $\angle 4$ forms a linear pair with $\angle 1$, so $\angle 4 = 90^\circ$, $\angle 2 + \angle 4 > 90^\circ$.

Answer:

∠3, ∠5