Question

$m\angle 1 + m\angle 2 = 90^\circ$ | blank
$m\angle 2 = m\angle 3$ | definition of congruent angles
blank | substitution property of equality
$\angle 1$ is a complement of $\angle 3$ | blank

Explanation:

Step1: Identify first reason

The equation \( m\angle1 + m\angle2 = 90^\circ \) is the definition of complementary angles (if two angles sum to \( 90^\circ \), they are complementary). So the reason here is "Definition of complementary angles".

Step2: Apply Substitution Property

We know \( m\angle2 = m\angle3 \) and \( m\angle1 + m\angle2 = 90^\circ \). By Substitution Property, replace \( m\angle2 \) with \( m\angle3 \) in the first equation: \( m\angle1 + m\angle3 = 90^\circ \).

Step3: Identify last reason

Since \( m\angle1 + m\angle3 = 90^\circ \), by the definition of complementary angles, \( \angle1 \) is a complement of \( \angle3 \). So the reason here is "Definition of complementary angles".

Answer:

• First dashed box: Definition of complementary angles
• Third dashed box (under Substitution): \( m\angle1 + m\angle3 = 90^\circ \)
• Last dashed box: Definition of complementary angles