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Let's do a couple of examples
dealing with angles between

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parallel lines and
transversals.

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So let's say that these two
lines are a parallel, so I can

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a label them as being parallel.

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That tells us that they will
never intersect; that they're

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sitting in the same plane.

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And let's say I have a
transversal right here, which

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is just a line that will
intersect both of those

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parallel lines, and I were to
tell you that this angle right

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there is 60 degrees and then I
were to ask you what is this

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angle right over there?

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You might say, oh, that's
very difficult; that's

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on a different line.

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But you just have to remember,
and the one thing I always

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remember, is that corresponding
angles are always equivalent.

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And so if you look at this
angle up here on this top line

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where the transversal
intersects the top line, what

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is the corresponding angle to
where the transversal

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intersects this bottom line?

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Well this is kind of the bottom
right angle; you could see

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that there's one, two,
three, four angles.

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So this is on the bottom
and kind of to the

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right a little bit.

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Or maybe you could kind of view
it as the southeast angle

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if we're thinking in
directions that way.

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And so the corresponding
angle is right over here.

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And they're going
to be equivalent.

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So this right here
is 60 degrees.

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Now if this angle is 60
degrees, what is the

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question mark angle?

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Well the question mark angle--
let's call it x --the question

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mark angle plus the 60 degree
angle, they go halfway

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around the circle.

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They are supplementary; They
will add up to 180 degrees.

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So we could write x plus
60 degrees is equal

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to 180 degrees.

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And if you subtract 60 from
both sides of this equation you

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get x is equal to 120 degrees.

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And you could keep going.

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You could actually figure out
every angle formed between

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the transversals and
the parallel lines.

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If this is 120 degrees,
then the angle opposite to

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it is also 120 degrees.

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If this angle is 60 degrees,
then this one right here

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is also 60 degrees.

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If this is 60, then its
opposite angle is 60 degrees.

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And then you could either say
that, hey, this has to be

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supplementary to either this
60 degree or this 60 degree.

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Or you could say that this
angle corresponds to this 120

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degrees, so it is also 120, and
make the same exact argument.

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This angle is the same
as this angle, so it

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is also 120 degrees.

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Let's do another one.

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Let's say I have two lines.

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So that's one line.

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Let me do that in purple and
let me do the other line in a

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different shade of purple.

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Let me darken that other
one a little bit more.

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So you have that purple
line and the other one

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that's another line.

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That's blue or
something like that.

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And then I have a line that
intersects both of them; we

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draw that a little
bit straighter.

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And let's say that this angle
right here is 50 degrees.

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And let's say that I were also
to tell you that this angle

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right here is 120 degrees.

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Now the question I want to
ask here is, are these

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two lines parallel?

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Is this magenta line and
this blue line parallel?

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So the way to think about is
what would have happened

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if they were parallel?

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If they were parallel, then
this and this would be

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corresponding angles, and so
then this would be 50 degrees.

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This would have to
be 50 degrees.

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We don't know, so maybe I
should put a little asterisk

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there to say, we're not sure
whether that's 50 degrees.

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Maybe put a question mark.

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This would be 50 degrees if
they were parallel, but this

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and this would have to be
supplementary; they would have

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to add up to 180 degrees.

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Actually, regardless of whether
the lines are parallel, if I

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just take any line and I have
something intersecting, if this

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angle is 50 and whatever this
angle would be, they would have

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to add up to 180 degrees.

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But we see right here that this
will not add up to 180 degrees.

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50 plus 120 adds up to 170.

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So these lines aren't parallel.

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Another way you could have
thought about it-- I guess this

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would have maybe been a more
exact way to think about it

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--is if this is 120 degrees,
this angle right here has to be

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supplementary to that; it
has to add up to 180.

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So this angle-- do it in this
screen --this angle right

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here has to be 60 degrees.

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Now this angle corresponds
to that angle, but

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they're not equal.

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The corresponding angles
are not equal, so these

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lines are not parallel.

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