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CCSS Math: 4.G.A.1

Put the vertex of the angle
at point A. So let me do that. Make one of the rays
go through point B. Make the other ray go
through one of the other points to make an acute angle. So an acute angle is an
angle less than 90 degrees. So we could make one of these
rays go through point B. And then we have to pick where
to put the other ray to make it go to one of
the other points. And we have to be
very careful here because we have to look at
this arc that shows which angle the tool is
actually measuring. Because we might be tempted
to do something like this, thinking that, hey,
maybe this is the angle that we're thinking about. But the tool thinks we're
referring to this outer angle right over here, this
larger huge angle. This angle right over here
is well over 180 degrees. So we have to pay
attention to this arc to make sure that the tool
is looking at the same angle that we are. So once again, we
want an acute angle. So this right over here
looks like an acute angle. It looks like it is
less than 90 degrees. And we have to be very
careful that we go exactly through that point. So that looks about right. This is an acute angle
because its measure is less than 90 degrees. Let's do a few more of these. Make an obtuse angle
using the black points. Choose one of the
points as the vertex and make the rays go through
the other two points. The angle should also be
less than 180 degrees. So you could think
of it several ways. You could just try
to pick that point. But then when you go through
these other two points, this right over here
is an acute angle. This is less than 90 degrees. You could do something
like this where now when I switch the rays, the tool is
now thinking about this angle, not this outer angle
right over here. But this is larger
than 180 degrees. So this also doesn't apply. So we really picked the
wrong point for the vertex. If you just move this out
of the way and eyeball it, it looks like you get
the largest angle that's less than 180 degrees if you
put the vertex right over here. So let me do that. Put the vertex right over there. And now it looks like I have
constructed a 180-degree angle. And we have to be
very careful that we go right through those
points because otherwise it might mark us wrong. So that looks pretty good. That's an obtuse angle
because its measure is greater than 90 degrees. Let's do one more of these. So another obtuse
angle using the points. Same general idea so that would
be an exactly 180-degree angle. And there we go. And this is an obtuse
angle because it is greater than 90 degrees.