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## Missing angle problems

## Video transcript

Let's say we have two
intersecting lines. So that's one of the
lines right over there. And then I have another
line right over here. So those are my two
intersecting lines. And let's say we know that
the measure of this angle right over here is
equal to 7x plus 182. And this is being
given in degrees, so it's 7x plus 182 degrees. And we know that the measure
of this angle right over here is 9x plus 194 degrees. So my question to
you is, what is the measure of each
of these angles? And I encourage you to pause
the video and to think about it. Well, the thing that
might jump out at you is that these two things
are vertical angles. They're the opposite angles
when we have these intersecting lines right over here. And vertical angles are
equal to each other. So we know, because these
are vertical angles, that 9x plus 194 degrees must
be equal to 7x plus 182 degrees. And now we just
have to solve for x. So if we want all the x-terms
on the left-hand side, we could subtract 7x from here. We've got to do it to
both sides, of course, in order to maintain
the equality. And then we could put
all of our constant terms on the right-hand side. So we can subtract
194 from the left. We have to subtract
194 from the right in order to maintain
the inequality. And on the left, what
we're left with is just 2x. And on the right, what
we're left with-- let's see. 182 minus 194. So if it was 194 minus 182,
it would be positive 12. But now it's going
to be negative 12. We're subtracting the
larger from the smaller, so it's equal to negative 12. And then divide both sides by 2. And we get x is
equal to negative 6. And now we can use
that information to find out the measure of
either one of these angles, which is the same
as the other one. So we can see here that if we
take 7 times negative 6 plus 182, so 7 times negative
6 is negative 42, plus 182 is going to be
equal to 140 degrees. And you'll see the
same thing over here. If we say 9 times negative 6,
which is negative 54, plus 194, this also equals 140 degrees.