To analyze the statements and determine the reasons behind each statement, we can organize the relationships between the angles and deduce the reasons using properties of complementary angles and equality of angles.
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Statement: \(\angle 1\) and \(\angle 2\) are complementary.
Reason: Definition of complementary angles (if two angles are complementary, their measures add up to 90°). -
Statement: \(m\angle 1 + m\angle 2 = 90°\).
Reason: By the definition of complementary angles, since \(\angle 1\) and \(\angle 2\) are complementary. -
Statement: \(\angle 1 \cong \angle 4\).
Reason: Given (or can depend on the specific diagram or information provided indicating that these angles are equal). -
Statement: \(\angle 2 \cong \angle 3\).
Reason: Given or based on angle congruence or relationship described in the problem. -
Statement: \(m\angle 2 = m\angle 3\).
Reason: If two angles are congruent, their measures are equal (definition of congruent angles). -
Statement: \(m\angle 3 + m\angle 3 = 90°\).
Reason: If \(\angle 3\) is related to another angle (such as being complementary to another angle), but this appears to be an error—you'd typically see something like \(m\angle 3 + m\angle 4 = 90°\) or \(m\angle 3 + m\angle 5 = 90°\) if relates to complementary angles. -
Statement: \(\angle 3\) and \(\angle 4\) are complementary.
Reason: Definition of complementary angles (based on prior angle relationships that leads to this conclusion).
In summary, the primary reasons for each statement rely on the definitions of complementary angles and the congruency of angles, along with the transitive property of equality when applicable. To confirm the validity of these statements and their relationships, a diagram or additional contextual information may help in clarifying the specific relationships and properties being used.