Angles of parallel lines 2

Angles of parallel lines examples

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

parallel lines and
transversals.

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

a label them as being parallel.

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

sitting in the same plane.

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

is just a line that will
intersect both of those

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

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

angle right over there?

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

on a different line.

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

remember, is that corresponding
angles are always equivalent.

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

where the transversal
intersects the top line, what

is the corresponding angle to
where the transversal

intersects this bottom line?

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

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

So this is on the bottom
and kind of to the

right a little bit.

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

if we're thinking in
directions that way.

And so the corresponding
angle is right over here.

And they're going
to be equivalent.

So this right here
is 60 degrees.

Now if this angle is 60
degrees, what is the

question mark angle?

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

mark angle plus the 60 degree
angle, they go halfway

around the circle.

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

So we could write x plus
60 degrees is equal

to 180 degrees.

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

get x is equal to 120 degrees.

And you could keep going.

You could actually figure out
every angle formed between

the transversals and
the parallel lines.

If this is 120 degrees,
then the angle opposite to

it is also 120 degrees.

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

is also 60 degrees.

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

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

supplementary to either this
60 degree or this 60 degree.

Or you could say that this
angle corresponds to this 120

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

This angle is the same
as this angle, so it

is also 120 degrees.

Let's do another one.

Let's say I have two lines.

So that's one line.

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

different shade of purple.

Let me darken that other
one a little bit more.

So you have that purple
line and the other one

that's another line.

That's blue or
something like that.

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

draw that a little
bit straighter.

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

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

right here is 120 degrees.

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

two lines parallel?

Is this magenta line and
this blue line parallel?

So the way to think about is
what would have happened

if they were parallel?

If they were parallel, then
this and this would be

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

This would have to
be 50 degrees.

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

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

Maybe put a question mark.

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

and this would have to be
supplementary; they would have

to add up to 180 degrees.

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

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

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

to add up to 180 degrees.

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

50 plus 120 adds up to 170.

So these lines aren't parallel.

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

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

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

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

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

here has to be 60 degrees.

Now this angle corresponds
to that angle, but

they're not equal.

The corresponding angles
are not equal, so these

lines are not parallel.