Question

which angles are complementary to ∠1? select all that apply. ∠4 ∠5 ∠6 ∠2

Explanation:

Step1: Define complementary angles

Complementary angles sum to $90^\circ$.

Step2: Use right angle property

$\angle 2$ is a right angle ($90^\circ$), so $\angle 1 + \angle 4 = 90^\circ$.

Step3: Use vertical angles

$\angle 4$ and $\angle 1$'s complement: $\angle 6$ is vertical to $\angle 2$? No, $\angle 5$ is vertical to $\angle 2$? No, $\angle 4$ and $\angle 6$: $\angle 1$ and $\angle 6$: since $\angle 5 = 90^\circ$, $\angle 1 + \angle 6 = 90^\circ$.
Wait, correction: $\angle 2$ is $90^\circ$, so $\angle 1 + \angle 4 = 90^\circ$ (they form $\angle 2$). Also, $\angle 4$ and $\angle 6$ are vertical? No, $\angle 1$ and $\angle 4$'s vertical pair? $\angle 6$ is equal to $\angle 4$ (vertical angles), so $\angle 1 + \angle 6 = 90^\circ$.

Step4: Verify each angle

• $\angle 4$: $\angle 1 + \angle 4 = 90^\circ$ → complementary
• $\angle 5$: $\angle 5 = 90^\circ$, $\angle 1 + 90^\circ

eq 90^\circ$ → not complementary

• $\angle 6$: $\angle 6 = \angle 4$ (vertical angles), so $\angle 1 + \angle 6 = 90^\circ$ → complementary
• $\angle 2$: $\angle 2 = 90^\circ$, $\angle 1 + 90^\circ

eq 90^\circ$ → not complementary

Answer:

$\angle 4$, $\angle 6$