Question

1. given ∠1 is a complement of ∠2. ∠2≅∠3 prove ∠1 is a complement of ∠3.

Explanation:

Step1: Recall the definition of complementary angles

If $\angle1$ is a complement of $\angle2$, then $\angle1+\angle2 = 90^{\circ}$.

Step2: Use the given congruence

Since $\angle2\cong\angle3$, then $\angle2=\angle3$ (congruent angles have equal measures).

Step3: Substitute $\angle2$ with $\angle3$

Substitute $\angle2$ in the equation $\angle1+\angle2 = 90^{\circ}$ with $\angle3$. We get $\angle1+\angle3=90^{\circ}$.

Step4: Apply the definition of complementary angles again

By the definition of complementary angles (two angles whose sum is $90^{\circ}$ are complementary), $\angle1$ is a complement of $\angle3$.

Answer:

Since $\angle1+\angle2 = 90^{\circ}$ and $\angle2=\angle3$, then $\angle1+\angle3 = 90^{\circ}$, so $\angle1$ is a complement of $\angle3$.