Question

given: ∠1 and ∠2 form a linear pair; m∠1 = m∠3
prove: ∠2 and ∠3 are supplementary
statements reasons

1. ∠1 and ∠2 form a linear pair; m∠1 = m∠3 1. given
2. ∠1 and ∠2 are supplementary 2.
3. 3. defn. of supplementary ∠s
4. m∠3 + m∠2 = 180° 4.
5. ∠2 and ∠3 are supplementary 5.

Explanation:

Step1: Recall linear - pair property

If two angles form a linear pair, they are supplementary. So, since $\angle1$ and $\angle2$ form a linear pair, $\angle1$ and $\angle2$ are supplementary.

Step2: Write the supplementary - angle equation

By the definition of supplementary angles, $m\angle1 + m\angle2=180^{\circ}$.

Step3: Substitute $\angle1$ with $\angle3$

Given that $m\angle1 = m\angle3$, we substitute $m\angle1$ in the equation $m\angle1 + m\angle2 = 180^{\circ}$ to get $m\angle3 + m\angle2=180^{\circ}$.

Step4: Use the definition of supplementary angles

If the sum of the measures of two angles is $180^{\circ}$, then the two angles are supplementary. Since $m\angle3 + m\angle2 = 180^{\circ}$, $\angle2$ and $\angle3$ are supplementary.

Answer:

Statements	Reasons
2. $\angle1$ and $\angle2$ are supplementary	2. If two angles form a linear pair, they are supplementary
3. $m\angle1 + m\angle2=180^{\circ}$	3. Defn. of Supplementary $\angle$'s
4. $m\angle3 + m\angle2 = 180^{\circ}$	4. Substitution property ($m\angle1 = m\angle3$)
5. $\angle2$ and $\angle3$ are supplementary	5. If the sum of the measures of two angles is $180^{\circ}$, the angles are supplementary