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## Vertical, complementary, and supplementary angles

# Angle relationships example

## Video transcript

We're asked to name an
angle adjacent to angle BGD. So angle BGD, let's see
if we can pick it out. So here is B, here is G, and
here is D, right over here. So angle BGD is this entire
angle right over here. So when we talk about
adjacent angles, we're talking
about an angle that has one of its rays in common. So for example, angle AGB has
one of the rays in common, it has GB in common
with angle BGD. So we could say angle AGB,
which could obviously also be called angle
BGA, BGA and AGB are both this angle right over here. You could also go
with angle FGB, because that also
has GB in common. So you go angle FGB, which could
also be written as angle BGF. Or you could go over here, angle
EGD shares ray GD in common. So you could do this angle
right over here, angle EGD. Or you could go all the
way out here, angle FGD. These last two sharing
ray GD in common. So any one of these responses
would satisfy the question of just naming an
angle, just naming one. Let's do this next one. Name an angle
vertical to angle EGA. So this is this angle
right over here. And the way you think
about vertical angles is, imagine two lines crossing. So imagine two lines
crossing, just like this. And they could
literally be lines, and they're
intersecting at a point. This is forming
four angles, or you could imagine it's forming
two sets of vertical angles. So if this is the angle
that you care about, it's a vertical
angle, it's the one on the opposite side
of the intersection. It's one of these angles
that it is not adjacent to. So it would be this
angle right over here. So going back to the question,
a vertical angle to angle EGA, well if you imagine
the intersection of line EB and line DA,
then the non-adjacent angle formed to angle
EGA is angle DGB. Actually, what we already
highlighted in magenta right over here. So this is angle DGB. Which could also be
called angle BGD. These are obviously both
referring to this angle up here. Name an angle that forms a
linear pair with the angle DFG. So we'll put this
in a new color. Angle DFG. Sorry, DGF, all of these
should have G in the middle. DGF. So linear pair with
angle DGF, so that's this angle right over here. So an angle that forms a linear
pair will be an angle that is adjacent, where the two outer
rays combined will form a line. So for example, if you
combine angle DGF, which is this angle, and angle DGC,
then their two outer rays form this entire
line right over here. So we could say angle DGC. Or, if you look at angle DFG,
you could form a line this way. If you take angle AGF,
so if you take this one, then the outer rays
will form this line. So angle AGF would also work. Angle AGF. Let's do one more. Name a vertical
angle to angle FGB. So this is FGB right over here. You could imagine this angle is
one of the four angles formed when CF-- let me highlight
this, that's hard to see. This is the last one, so I
can make a mess out of this. That angle is formed when CF and
EB intersect with each other. And four angles are formed. The one question, FGB, these two
angles that are adjacent to it, it shares a common ray. And then the vertical
angle, the one that sits on the opposite side. So this angle, this angle right
over here, which is angle EGC. Or you could also
call it angle CGE. So angle CGE.