Question

given: ∠1 and ∠2 are supplementary and ∠3 and ∠2 are supplementary. prove: ∠1 ≅ ∠3 use the reasons to complete the proof. definition of congruence substitution given subtraction property of equality statements reasons m∠1 + m∠2 = 180 m∠3 + m∠2 = 180 m∠1 + m∠2 = m∠3 + m∠2 m∠1 = m∠3 ∠1 ≅ ∠3

Explanation:

Step1: Recall supplementary - angle definition

Since $\angle1$ and $\angle2$ are supplementary, by the definition of supplementary angles, $m\angle1 + m\angle2=180$. The reason is "Given".

Step2: Recall supplementary - angle definition

Since $\angle3$ and $\angle2$ are supplementary, by the definition of supplementary angles, $m\angle3 + m\angle2 = 180$. The reason is "Given".

Step3: Substitute equal values

Because $m\angle1 + m\angle2=180$ and $m\angle3 + m\angle2 = 180$, we can substitute to get $m\angle1 + m\angle2=m\angle3 + m\angle2$. The reason is "Substitution".

Step4: Apply subtraction property

Subtract $m\angle2$ from both sides of the equation $m\angle1 + m\angle2=m\angle3 + m\angle2$. By the subtraction property of equality, we get $m\angle1=m\angle3$. The reason is "Subtraction Property of Equality".

Step5: Use congruence definition

Since $m\angle1=m\angle3$, by the definition of congruent angles (angles with equal measures are congruent), $\angle1\cong\angle3$. The reason is "Definition of Congruence".

Answer:

Statements	Reasons
$m\angle3 + m\angle2 = 180$	Given
$m\angle1 + m\angle2=m\angle3 + m\angle2$	Substitution
$m\angle1=m\angle3$	Subtraction Property of Equality
$\angle1\cong\angle3$	Definition of Congruence