Question

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Explanation:

Step1: Identify the first blank

Supplementary angles are defined as two angles whose sum is 180 degrees. Since ∠1 and ∠2 are supplements, the first blank is "supplementary".

Step2: Identify the second blank

Given that ∠3 and ∠2 are supplements, the sum of ∠3 and ∠2 is 180 degrees. So the second blank is "3 and 2".

Step3: Identify the third blank

We have \( m\angle1 + m\angle2 = 180^\circ \) and \( m\angle3 + m\angle2 = 180^\circ \). By the transitive property (or substitution property, since both equal \( 180^\circ \)), we can say \( m\angle1 + m\angle2 = m\angle3 + m\angle2 \). So the third blank is "transitive" (or "substitution").

Step4: Identify the fourth blank

To get \( m\angle1 = m\angle3 \), we subtract \( m\angle2 \) from both sides. So the fourth blank is "2".

Answer:

First blank: supplementary; Second blank: 3 and 2; Third blank: transitive (or substitution); Fourth blank: 2