geometry proofs-?

Question

need to write as to colum with statement and reasons

***NOTE < is the angle sign.

Given:
< 1 is a supplement of < 2
<3 is a supplement of < 4
m < 2 = m < 4

Prove:
m<1 = m<3

was told there were eight steps

Answer 1

< 1 + < 2 = 180 degrees ..... definition of supplementary <'s
< 3 + < 4 = 180 degrees ..... definition of supplementary <'s
< 1 + < 2 = < 3 + < 4 .... transitive or (substitution) property
< 2 = < 4 .... given
< 1 + < 4 = < 3 + < 4 ...... substitution
< 1 + < 4 - < 4 = < 3 + < 4 - < 4.... subtraction property of equality
< 1 = < 3

Answer 2

Proof:

<2 = <4 Given
<1 = 180 deg - <2 Supplementary Angles
<3 = 180 deg - < 4 Supplementary Angles

Therefore <1 = <3 Substitution or Transitive

Answer 3

I think you should do this for yourself. For one thing, it sounds so prescriptive that what I write might be different from what your teacher expects!

It's almost obvious. If you let x = m(<1), and y = m(<3), then clearly

x = 180 deg - y

Let p = m(<3), and we don't have to write anything for m(<4) as we're told it's y.

We're also told
p = 180 deg - y (<3 is the (NOT "a" supplement -- there's only one!) supplement of <4),

which proves x = p.

Of course, you could do this without using x, y etc, but if you're supposed to spin something so simple and obvious out into eight lines I guess the "let x = " etc could make up a few of the lines.

Answer 4

supplement so <1 is supplement to <2 if the measure adds together to equal 180 and the same with <3 and <4 and if <2 =<4 then <1 has to equal <3 (if it is shaped like an X ) because of vertical angles Angles that are verticaly across from each other have the same measure
Hope it helps, i hated proofs