Can someone help me with a really easy math problem?

Question

anonymous · Answer

attachment

anonymous · Answer

@ParthKohli Can you help me out?

parthkohli · Answer

idk what statement 1 is for. the statement 4 is the thing we needed to prove. what do you think the reasons are?

anonymous · Answer

This is what I've figured out so far. I need help figuring out the reasoning for 3 and 4. I also need someone to check over my answers for what I already did. 

1. <2 and <5 are supplementary 
1. given 
2. vertical angles 
3. ?
4. l||m 
4. ?

parthkohli · Answer

if <2 and <5 are supplementary
and <3 = <2
then <3 and <5 are supplementary

anonymous · Answer

They give me <3 = <2 but I need a reasoning for it. I know there's a reason that <3 = <2 but I'm not sure what the reasoning is.

parthkohli · Answer

you wrote "vertical angles" for 2 didn't you

anonymous · Answer

Oh... I did. Sorry I wasn't thinking. I already solved that part. Never mind.

anonymous · Answer

So how do you solve the reasoning for 3 and 4?

parthkohli · Answer

I wrote that above

parthkohli · Answer

if <2 and <5 are supplementary
and <3 = <2
then <3 and <5 are supplementary

anonymous · Answer

Is there like a theorem to explain what you just wrote? and is that the answer for 3 or 4?

parthkohli · Answer

<2 + <5 = 180
<2 = <3

eliminate <2 from these two equations

anonymous · Answer

What do you mean?