Question

∠1 and ∠3 are complementary 1 given
2 2 definition of complementary angles
3 3
4 4
5 ∠2≅∠3 5
m∠1 + m∠2 = 90°
:: m∠2 = m∠3
:: m∠1 + m∠3 = 90°
:: m∠1 + m∠2 = m∠1 + m∠3
:: definition of congruent angles
:: subtraction property of equality
:: transitive property of equality

Explanation:

Step1: Apply definition of complementary angles

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

Step2: Assume $\angle1$ and $\angle2$ are also complementary (missing - but needed for proof)

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

Step3: Set the two equations equal (Transitive Property of Equality)

$m\angle1 + m\angle2=m\angle1 + m\angle3$

Step4: Use Subtraction Property of Equality

$m\angle2=m\angle3$

Step5: Use Definition of congruent angles

$\angle2\cong\angle3$

Answer:

1. $m\angle1 + m\angle3 = 90^{\circ}$
2. Assume $m\angle1 + m\angle2 = 90^{\circ}$
3. $m\angle1 + m\angle2=m\angle1 + m\angle3$ (Transitive Property of Equality)
4. $m\angle2=m\angle3$ (Subtraction Property of Equality)