Question

question 35 of 49
what is another way to summarize the outcome of this proof?
given: line ae intersects rv at point n.
prove: ∠anr and ∠vne are congruent.
statements reasons
line ae intersects rv at point n. given statement.
m∠anv + m∠vne = 180 definition of linear - pair:
these two angles form a linear pair, so their
measures sum to 180 degrees.
m∠anv = 180 - m∠vne subtraction:
m∠vne is subtracted from both sides of the
equation.
m∠anv + m∠anr = 180 these two angles also form a linear pair, so their
measures sum to 180 degrees.
(180 - m∠vne)+m∠anr = 180 substitution:
substitution of equivalent form for m∠anv from
step 3 of proof.
m∠anr = m∠vne simplifying of the equation by subtracting 180 from
both sides and adding m∠vne to both sides.
∠anr ≅ ∠vne definition of congruent angles:
these angles have the same measure, so by
definition, they are congruent.
qed
a. vertical angles are supplementary.
b. angles forming a linear pair are supplementary.
c. angles forming a linear pair are congruent.
d. vertical angles are congruent.

Explanation:

The proof shows that ∠ANR and ∠VNE which are vertical - angles are congruent. It starts with the properties of linear pairs and through a series of algebraic manipulations and use of angle - related definitions, concludes that the vertical angles have the same measure and are thus congruent.

Answer:

D. Vertical angles are congruent.