Diana and joby wrote the following proofs to prove that vertical angles are congruent. who is correct?

diana's proof

statement justification

∠1 + ∠2 = 180° definition of supplementary angles

∠1 + ∠4 = 180° definition of supplementary angles

∠1 + ∠2 = ∠1 + ∠4 transitive property of equality

joby's proof

statement justification

∠2 = ∠4 vertical angles are congruent.

∠1 = ∠3 vertical angles are congruent.

vertical angles are congruent. vertical angle theorem

a. diana is correct, but joby is not.
b. both diana and joby are correct.
c. neither diana nor joby is correct.
d. joby is correct, but diana is not.

Diana is correct Joby is not.

Step-by-step explanation:

To prove that vertical angles are congruent.

DIana started with linear pair property of supplementary angles for two lines

and used transitive property to prove that vertically opposite angles are equal

Hence Diana proof is correct.

But Joby's proof contains these following errors

Instead of proving vertical angles equal, he has used them in the first step as given.  This is wrong  Similarly second statement also is to be proved but he simply stated without any justification

these sign is used to tell weather the number is greater or less than the number   <   or >     but this sign means its equal =    

hope this you and

step-by-step explanation: