Question

by the linear pair theorem, ∠2 is supplementary to ∠3, which means ( mangle2 + mangle3 = 180^circ ). it is given that ( angle3 cong angle4 ), so by the definition of congruent angles, ( mangle3 = mangle4 ). using the substitution property of equality, substitute ( mangle4 ) in for ( mangle3 ) to rewrite the previous equation as ( mangle2 + mangle4 = 180^circ ). thus ( angle2 ) is supplementary to ( angle4 ) by the definition of supplementary angles. by the linear pair theorem, ( angle1 ) is supplementary to ( angle4 ). since ( angle2 ) and ( angle1 ) are supplementary to ( angle4 ), then by the congruent supplements theorem, ( angle1 cong angle2 ).
use the paragraph proof to complete the two - column proof.
what statement and reason belong in line 5?

statements	reasons
2. ( mangle2 + mangle3 = 180^circ )	2. definition of supplementary angles
3. ( angle3 cong angle4 )	3. given
4. ( mangle3 = mangle4 )	4. definition of congruence
5.	5.
6.	definition of supplementary angles
7. angle 3 is supplementary to angle 4	linear pair theorem
8. the angle sum of 2 and 4 is 180 degrees<br>the angle sum of 3 and 4 is 180 degrees<br>angle 1 is supplementary to angle 3	congruent supplements theorem

Explanation:

Step1: Identify substitution step

From the paragraph proof, we substitute $m\angle4$ for $m\angle3$ in the supplementary angle equation.

Step2: Write the substituted statement

$m\angle2 + m\angle4 = 180^\circ$

Step3: Match the reason

The reason for this step is the substitution property of equality, which lets us replace congruent angle measures.

Answer:

Statement: $m\angle2 + m\angle4 = 180^\circ$
Reason: substitution property of equality