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## Geometry (all content)

### Course: Geometry (all content)>Unit 2

Lesson 6: Vertical, complementary, and supplementary angles

# Angle relationships example

Sal finds a linear pair, vertical angles, and adjacent angles from a diagram. Created by Sal Khan.

## Want to join the conversation?

• Can two vertical angles also be adjacent?
(8 votes)
• No, they cannot because they are angles opposite to each other.
(3 votes)
• are there fun ways to memorize the angles
(4 votes)
• You could make flashcards, memorize them in creative ways, or whatnot. It all depends if you truly put your mind to it.
(1 vote)
• At , couldn't angle <AGD be adjacent to angle <BGD? Doesn't <AGD have <GD in it?
(3 votes)
• The term "adjacent" means that the angle must be next to the designated angle (in this case, <BGD). The adjacent angle cannot contain (in part or in whole) the original angle in which you are comparing to (In short, no overlapping). Because <AGD contains the whole <BGD, <AGD cannot be adjacent to <BGD. As said in the video, some examples include <AGB and <EGD.
(2 votes)
• How is it angle DGF a linear pair with DGC?
(2 votes)
• The concept of linear pairs is that if there is a straight line and another line intersects the straight line at a point, then the two angles made by the other line are equal to 180 degrees. Since line CF is straight and line DA intersects CF at point G, so angle CGF is a straight angle. Then it's just angle CGF divided into 2 other angles, which are DGF and DGC, so they add up to 180 degrees, therefore becoming a linear pair. Hope that helps!
(1 vote)
• What do you call an angle whose measure is 90° ?
(2 votes)
• We call that a "right angle".
(1 vote)
• <ABG can also be called <BAG? ignore the fact that spells Bag.
(2 votes)
• Nope, not really. The vertex has to be the middle letter, so for 3-letter notation there are 2 possible ways of naming the same angle:

∠BGA and ∠AGB

Angle ∠BAG is not on the picture. It would look like an angle with sides (rays) AB and AG and vertex A. By the way, ∠ABG is not on this picture either.

Edit: fixed.
(2 votes)
• what is the difference between acute and obtuse
(2 votes)
• An acute angle measures less than 90 degrees.
An obtuse angle measures more than 90 degrees.
Hope this helps.
(2 votes)
• For an angle to be supplementary does it have to be adjacent?
(1 vote)
• No. All that is necessary is that the angles add up to be 180° (or π radians). They can be adjacent, or just different parts of the same shape or they can be on different continents in separate geometry books.

That said, you should definitely ask this question of your geometry teacher, who might have a different opinion, to avoid being marked wrong on a problem.
(3 votes)
• could angle CGB and CGD be adjacent angles to BGD
(2 votes)
• No; they overlap with/are part of BGD and cannot be considered adjacent.
(1 vote)
• so at , an angle that forms a linear pair with another angle means that the two angles hen added together make a 180 degree line ?
(2 votes)
• Well, that's a strange way to say it. 2 linear angles add up to 180 degrees because 180 degrees is the angle swept by either side of a line.
(1 vote)

## 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.