👉 Learn how to solve for an unknown variable using parallel lines and a transversal theorems. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated in both lines.
A transversal is a straight line crossing two parallel lines. There are various angle relationships formed when a transversal crosses two parallel lines. They include: alternate interior angles, alternate exterior angles, corresponding angles, consecutive interior angles, etc.
The theorems of the angle relationships include: alternate interior angles are equal, alternate exterior angles are equal, consecutive interior angles are supplementary (equal to 180 degrees), corresponding angles are equal.
Given expressions representing the angles formed by two parallel lines and a transversal, we can make use of the parallel line/ transversal angle relationships and usual angle properties to solve for the unknown variable in the expressions.
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okay so in this case ladies and
gentlemen um I
believe what they told us for this one
is now we know we have um parallel lines
correct in this example they gave us
parall lines and what they asked us to
do was now to go ahead and determine uh
Blake what our um angle relationship was
so ladies and gentlemen we're going to
be doing these problems and you'll see a
lot why it's more so important today but
when you're applying these problems it's
going to become very important Camilo
with for you to make sure you write down
the relationship that you are working
with so right now we have these three
angles all right and we also have two
different variables all right you can
see we have x's and we have a y so what
we want to do is we want to be able to
determine what is the relationship
between the angles with just the
variable X and when I look at Taylor and
she goes and thinks about that what
relationship would you say these two
angles have alternate inter alternate
interior angles and since we have
parallel lines alternate interior angles
are how do they relate to each other
conent they are congruent that's right
they have the exact same
measure um I'll just do alt interior
angles so we have alter interior angles
so therefore it's 8x - 10 =
7X right so now can we find the value of
x Sam right we now we have an equation
so of course can so we can just get the
X on the same side so if I have x - 10 =
0 and then add the 10 to the other side
so x = 10 right cool now we found the x
equal 10 but we're not done yet because
now all right if we know that x equals
10 then this angle would be 7x which
would be 7 * 10 therefore we could say
that that angle is wor is equal to
70° right so rather than just writing 7x
let's write in this angle as 70
and the reason why I do that is because
now I see all right I need to still
figure out this value of y and if I'm
going to figure out the value of my
variable y I need to know what that
value of x is so then I go and look at
Mario and say Mario these two
angles how are these two angles related
to each other the same L they're on the
same line well they create a they create
a line too right so what was that angle
how do what definition or um what
vocabulary did we have when we had two
angles that created a line made up there
right next to each other
do you
remember Kaye you
remember
no uh well they don't have to do with
anything a par lines they make up this
par line Asia do you
remember how are these two angles
related to each
other okay so you guys are right on the
linear pair but you guys remember how do
linear pair what is they are a linear
pair that's exactly right they
are um they make up a line they share a
um vertex and a side so they are
adjacent so they are a linear pair but
what are a linear
pair yeah equal to 18 the sum of them is
equal to 180 so we call them what
supplementary angles yes they are linear
pair but the more importantly is you
need to understand they're supplementary
so
therefore I'll write down these are
supplementary angles
therefore I know that the sum of 6 y +
20 plus
70 equals 110 or
180° does that make sense okay no where'
I lose you you don't understand how
these are add to
180 these two angles the sum of these
two angles add up to 180 so they're
supplementary so we add them up to equal
to 180
these two name alternate interior angles
are equal to each other notice how I'm
giving you guys the definition before
I'm doing any of my work which is very
very important so therefore now I can
combine this up so I have 6 y um+ 90 =
180 now can I solve for
y yeah of course Zach right so I
subtract 90 on both sides and I have 6 y
= 90 then I divide by six
all right so by applying alternate
interior angles I was able to determine
that X is going to equal to 10 and then
by uh um determining for uh solving for
y by using sub angles I can determine Y
is going to
equal
15 and there you go okay so ladies and
gentlemen if uh you
