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Lesson 3: Vertical, complementary, and supplementary angles

# Vertical angles

By using our knowledge of supplementary, adjacent, and vertical angles, we can solve problems involving the intersection of two lines. Including this one! Created by Sal Khan.

## Want to join the conversation?

• What is the difference between intercept and intersecting? anyone? •   Intercept and intersect are similar terms used in different math subjects. An intercept, as in x or y intercept, is a term commonly used in graphing, where a line crosses your y or x axis at zero. An intersection is used in geometry, where a line segment or a ray crosses another. Hope this helped!
• What are adjacent, supplementary and complimentary angles? anyone? •  Supplementary angles are two angles whose angle measures sum to 180 degrees. For example, if one angle is 120 degrees and another angle is 60 degrees, the two angles are supplementary. Complementary angles are two angles whose angle measures sum to 90 degrees. For example, if one angle is 30 degrees and another angle is 60 degrees, the two angles are complementary. Adjacent angles share a side, share a vertex, and don't overlap. This link might help you picture adjacent angles. https://www.mathsisfun.com/geometry/adjacent-angles.html
• How is CEF adjacent () ? • This is hard. Idu.-I don't understand. Can someone explain me?
(1 vote) •  In supplementary angles the sum of 2 angles should be equal to 180
For example.... 60°+120° =180°
70°+110°=180°
AND SO ON

in this question the angle <BED = 70° which is already given

To find the measure of BEC
which can be take out very easily as both angles are supplementary so we can find it by

70°+_____=180°
Which is equal to 110°

And the angles which are in front of each other are always equal

Hope it helps🥰

Thank you

Please vote if It helps ..........
• Can angles be complementary and/or supplementary without being adjacent? Thx in advance • I'm very confused about the whole thing. Can you please help me understand it a little bit more? That would be nice if you could do that for me. Thank you for time to help me understand even though I watched to video.

- Jordan Holmes • Hi Jordan.
I'm not sure which part of the video you need help with, so I'll go through each section.
Okay, let's start!

@ So we can see that the angles BED and CEB are adjacent. This means that they are next to each other. Also, we know that the line CED is straight. This is important, so remember it!
@ By supplementary, Sal means that they both add up to 180 degrees. So angle BED is 70 degrees, and both angles add up to 180 degrees, so we can safely say that angle CEB is 110 degrees.
@ Alright. So we know that angle CEB is 110 degrees. So what about angle CEA? Well, we know that the two angles are adjacent. And we also know that line AEB is straight. So again, we can conclude that angles CEB and CEA are supplementary. So, `180-110=70!` Hmm! That number looks familiar! It seems that angles CEA and BED are the same! We'll talk about this in the next section.
@ Because the angles are opposite each other in this diagram, they are called "vertical angles" Vertical angles are the same. So, as we can see, angles CEA and BED are vertical!
@ By applying this same rule, we see that angles CEB and AED are vertical too. So we can comfortably say that angle AED is 110 degrees. And to confirm, we can see that angles CEA and AED are supplementary, and so `180-70=110`
@ Finally, we can see that every semicircle adds up to 180 degrees, while every full circle adds up to 360 degrees. Also, every quarter circle adds up to 90 degrees.

Okay! I hope that sums up the video nicely! If you have any questions, feel free to ask them in the comments and I'll reply ASAP. Thanks for reading!
- Daniel
• So what is exactly a vertical angle? • How are angles:CEA and CEB Adjacent? They aren't connecting to one line.. • I still don't get the difference between the verticle angle v.s supplementary & complementary angles.  