WEBVTT

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Let's say that we have
two parallel lines.

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So that's one line
right over there,

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and then this is
the other line that

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is parallel to the first one.

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I'll draw it as
parallel as I can.

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So these two lines are parallel.

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This is the symbol
right over here

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to show that these two
lines are parallel.

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And then let me draw
a transversal here.

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So let me draw a transversal.

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This is also a line.

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Now, let's say that we know
that this angle right over here

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is 110 degrees.

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What other angles can
we figure out here?

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Well, the first thing
that we might realize

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is that, look, corresponding
angles are equivalent.

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This angle, the angle
between this parallel line

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and the transversal,
is going to be

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the same as the angle
between this parallel line

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and the transversal.

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So this right over here is
also going to be 110 degrees.

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Now, we also know that
vertical angles are equivalent.

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So if this is 110
degrees, then this angle

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right over here on the opposite
side of the intersection

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is also going to be 110 degrees.

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And we could use that
same logic right over here

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to say that if this
is 110 degrees,

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then this is also 110 degrees.

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We could've also
said that, look,

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this angle right over here
corresponds to this angle

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right over here so that they
also will have to be the same.

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Now, what about
these other angles?

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So this angle right over
here, its outside ray,

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I guess you could
say, forms a line

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with this angle right over here.

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This pink angle is supplementary
to this 110 degree angle.

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So this pink angle plus 110
is going to be equal to 180.

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Or we know that this pink angle
is going to be 70 degrees.

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And then we know that it's a
vertical angle with this angle

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right over here, so
this is also 70 degrees.

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This angle that's kind of
right below this parallel line

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with the transversal, the bottom
left, I guess you could say,

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corresponds to this bottom
left angle right over here.

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So this is also 70 degrees.

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And we could've also
figured that out by saying,

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hey, this angle is supplementary
to this angle right over here.

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And then we could use
multiple arguments.

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The vertical angle argument,
the supplementary argument two

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ways, or the corresponding
angle argument to say that,

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hey, this must be
70 degrees as well.