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Angle relationships example (video) | Angles | Khan Academy

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Angle relationships example (video) | Angles | Khan Academy

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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.

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Angle relationships example (video) | Angles | Khan Academy

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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.

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Two angles are Adjacent when they have a common side and a common vertex (corner point) and don't overlap.

Angle ABC is adjacent to angle CBD

Because:

they have a common side (line CB)

they have a common vertex (point B)

What Is and Isn't an Adjacent Angle

These ARE Adjacent Angles

they share a vertex and a side

NOT Adjacent Angles

they only share a vertex, not a side

NOT Adjacent Angles

they only share a side,
not a vertex

Don't Overlap!

ALSO the angles must not overlap.

NOT Adjacent Angles

angles a and b overlap

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Two angles are Adjacent when they have a common side and a common vertex (corner point) and don't overlap. Angle ABC is adjacent to angle CBD Because: they have a common side (line CB) they have a common vertex (point B) These ARE Adjacent Angles they share a vertex and a side NOT Adjacent Angles they only share a vertex, not a side NOT Adjacent Angles they only share a side, not a vertex ALSO the angles must not overlap.

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"Vertical" in this case means they share the same Vertex (corner point), not the usual meaning of up-down.

Example: a° and b° are vertical angles.

The interesting thing here is that vertical angles are equal:

a° = b°

(in fact they are congruent angles)

Have a play with them yourself. Notice how the 4 angles are actually two pairs of "vertical angles":

images/geom-vert-angles.js

Example: Find angles a°, b° and c° below:

Because b° is vertically opposite 40°, it must also be 40°

A full circle is 360°, so that leaves 360° − 2×40° = 280°

Angles a° and c° are also vertical angles, so must be equal, which means they are 140° each.

Answer: a = 140°, b = 40° and c = 140°.

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"Vertical" in this case means they share the same Vertex (corner point), not the usual meaning of up-down. The interesting thing here is that vertical angles are equal: a° = b° (in fact they are congruent angles) Have a play with them yourself.

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These two angles (140° and 40°) are Supplementary Angles, because they add up to 180°:

Notice that together they make a straight angle.

But the angles don't have to be together.

These two are supplementary because
60° + 120° = 180°

Play With It ...

(Drag the points)

images/geom-comp-supp.js?mode=supp

When the two angles add to 180°, we say they "Supplement" each other. comes from Latin supplere, to complete or "supply" what is needed

Complementary vs Supplementary

A related idea is Complementary Angles, they add up to 90°

How to remember which is which? Well, alphabetically they are:

Complementary add to 90°

Supplementary add to 180°

You can also think:

"C" of Complementary is for "Corner" (a Right Angle), and

"S" of Supplementary is for "Straight" (180° is a straight line)

Or you can think:

when you are right you get a compliment (sounds like complement)

"supplement" (like a vitamin supplement) is something extra, so is bigger

817, 1804, 5232, 5234, 818, 3303, 1805, 3304, 5235, 5236

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These two angles (140° and 40°) are Supplementary Angles, because they add up to 180°: Notice that together they make a straight angle. But the angles don't have to be together. These two are supplementary because 60° + 120° = 180° (Drag the points) images/geom-comp-supp.js?mode=supp When the two angles add to 180°, we say they "Supplement" each other.

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Two angles are Complementary when they
add up to 90 degrees (a Right Angle )

These two angles (40° and 50°) are Complementary Angles, because they add up to 90°:

Notice that together they make a right angle

But the angles don't have to be together.

These two are complementary because 27° + 63° = 90°

Play With It ...

(Drag the points)

images/geom-comp-supp.js?mode=comp

Right Angled Triangle

In a right angled triangle, the two non-right angles are complementary, because in a triangle the three angles add to 180°, and 90° has already been taken by the right angle.

When two angles add to 90°, we say they "Complement" each other.

Complementary comes from Latin completum meaning "completed" ...
because the right angle is thought of as being a complete angle.

Spelling: be careful, it is not "Complimentary Angle" (with an "i") ...
that would be an angle you get for free!

Complementary vs Supplementary

A related idea is Supplementary Angles - those add up to 180°

How to remember which is which? Well, alphabetically they are:

Complementary add to 90°

Supplementary add to 180°

You can also think:

"C" of Complementary is for "Corner" (a Right Angle), and

"S" of Supplementary is for "Straight" (180° is a straight line)

Or you can think:

when you are right you get a compliment (sounds like complement)

"supplement" (like a vitamin supplement) is something extra, so is bigger

5231, 5233, 819, 2109, 820, 2110, 5240, 9063, 3305, 3306

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Two angles are Complementary when they add up to 90 degrees (a Right Angle )