Figuring out angles between transversal and parallel lines | Geometry | Khan Academy

Figuring out angles between transversal and parallel lines | Geometry | Khan Academy


Let’s say that we have
two parallel lines. So that’s one line
right over there, and then this is
the other line that is parallel to the first one. I’ll draw it as
parallel as I can. So these two lines are parallel. This is the symbol
right over here to show that these two
lines are parallel. And then let me draw
a transversal here. So let me draw a transversal. This is also a line. Now, let’s say that we know
that this angle right over here is 110 degrees. What other angles can
we figure out here? Well, the first thing
that we might realize is that, look, corresponding
angles are equivalent. This angle, the angle
between this parallel line and the transversal,
is going to be the same as the angle
between this parallel line and the transversal. So this right over here is
also going to be 110 degrees. Now, we also know that
vertical angles are equivalent. So if this is 110
degrees, then this angle right over here on the opposite
side of the intersection is also going to be 110 degrees. And we could use that
same logic right over here to say that if this
is 110 degrees, then this is also 110 degrees. We could’ve also
said that, look, this angle right over here
corresponds to this angle right over here so that they
also will have to be the same. Now, what about
these other angles? So this angle right over
here, its outside ray, I guess you could
say, forms a line with this angle right over here. This pink angle is supplementary
to this 110 degree angle. So this pink angle plus 110
is going to be equal to 180. Or we know that this pink angle
is going to be 70 degrees. And then we know that it’s a
vertical angle with this angle right over here, so
this is also 70 degrees. This angle that’s kind of
right below this parallel line with the transversal, the bottom
left, I guess you could say, corresponds to this bottom
left angle right over here. So this is also 70 degrees. And we could’ve also
figured that out by saying, hey, this angle is supplementary
to this angle right over here. And then we could use
multiple arguments. The vertical angle argument,
the supplementary argument two ways, or the corresponding
angle argument to say that, hey, this must be
70 degrees as well.

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