What is the missing reason for the 5th step in the proof below?
Given: Line AE intersects RV at point N.
Prove: Vertical angles ZANR and ZVNE are congruent.
STATEMENTS
Line AE intersects RV at point N.
mzANV+mZVNE-180
mANV=180-m/VNE
m/ANV+mZANR=180
(180-mZVNE)+m/ANR=180
mZANR-m2VNE
ZANR ZVNE
REASONS
Given statement
Definition of linear pair:
These two angles forma linear pair, so their
measures sum to 180 degrees.
Subtraction:
m/VNE is subtracted from both sides of the
equation.
Definition of linear pair:
These two angles also form a linear pair, so their
measures sum to 180 degrees.
?
Simplify:
Simplifying of the equation by subti sting 180 from
both sides and adding mZVNE to both sides.
Definition of congruent angles:
These angles have the same measure, so by
definition, they are congruent.
QED
O A. Simplification of equation from previous step
OB. Definition of a linear pair
O C. Definition of complementary angles
OD. Substitution