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CCSS.Math:

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 can make one of these rays go through point B and then we could we have to pick where to where to put the other way 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 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 it 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 this is an acute angle because it's 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 when you go through these other two points this right over here is an acute angle this is less than 90 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 kind of you can kind of 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 180 degree angle it have to be very careful that we go right through those points because otherwise it might mark us might Marcus wrong so that looks pretty good that's an obtuse angle because it's measure is greater than 90 degrees let's do one more of these so another obtuse angle using the points same general idea 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