Question

∠2≅∠3
m∠1 + m∠2 = 90°
m∠2 = m∠3
m∠1 + m∠3 = 90°
∠1 is a complement of ∠3.
:: m∠1 + m∠3 = 90°
:: addition property of equality
:: definition of complementary angles
:: given
:: reflexive property of equality
:: symmetric property of equality

Explanation:

Step1: Given information

$\angle2\cong\angle3$ and $m\angle1 + m\angle2=90^{\circ}$

Step2: Use congruent - angle definition

Since $\angle2\cong\angle3$, by the definition of congruent angles, $m\angle2 = m\angle3$.

Step3: Apply substitution

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

Step4: Recall complementary - angle definition

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

Answer:

The reason for $m\angle1 + m\angle2 = 90^{\circ}$ is Given. The reason for $\angle1$ is a complement of $\angle3$ is Definition of complementary angles.