Question

proof

1. write a two - column proof.

given ( mangle1 = 115^{circ} ) and ( mangle2 = 65^{circ} )
prove ( mparallel n )
two - column proof

statements	reasons
2. ( mangle1 + mangle2 = mangle1 + mangle2 )	2.
3. ( mangle1 + mangle2 = 115^{circ}+65^{circ} )	3.
4. ( mangle1 + mangle2 = 180^{circ} )	4.
5. ( angle1 ) and ( angle2 ) are supplementary.	5.
6. ( mparallel n )	6.

reasons bank
definition of supplementary angles, given
consecutive interior angles converse, substitution property of equality
reflexive property of equality, simplify

Explanation:

Step1: Match given statements

Reason: Given

Step2: Apply reflexive equality property

Reason: Reflexive Property of Equality

Step3: Substitute angle measures

Reason: Substitution Property of Equality

Step4: Calculate sum of angles

Reason: Simplify

Step5: Define supplementary angles

Reason: Definition of supplementary angles

Step6: Use converse theorem for parallel lines

Reason: Consecutive Interior Angles Converse

Answer:

STATEMENTS	REASONS
2. $m\angle1 + m\angle2 = m\angle1 + m\angle2$	2. Reflexive Property of Equality
3. $m\angle1 + m\angle2 = 115^\circ + 65^\circ$	3. Substitution Property of Equality
4. $m\angle1 + m\angle2 = 180^\circ$	4. Simplify
5. $\angle1$ and $\angle2$ are supplementary.	5. Definition of supplementary angles
6. $m \parallel n$	6. Consecutive Interior Angles Converse