# Complementary, Supplementary, and Vertical Angles

Welcome to a lesson on pairs of angles.

More specifically we’ll be talking about complementary, supplementary and vertical

angles. As well as solving problems involving

pairs of angles. Let’s first talk about adjacent angles.

Adjacent angles share the same vertex and share one side

but do not overlapped. So looking at this diagram here, angle 1 and angle 2 are adjacent angles. Well remember we can identify angle 1 as

angle ABC. And we can identify angle 2 as angle

CBD. And these 2 angles are adjacent

angles. I also wana point out there’s a

third angle. sketched here. It would be angle ABD. and the measure of angle ABD would be the

sum of the measure of angle 1 and angle 2. Looking at the second diagram here angle 3 and angle 4 are adjacent angles. Which

could also be identified by angle EFG and angle HFG. Remember when identifying

an angle using this notation, is important that the vertex be in the middle. Complementary angles are two angles that add to 90

degrees. Looking at that angle here formed by the

two black rays Notice this little square here indicates it’s a right angle. Which means it measures 90 degrees. And angle 5 and angle 6 are two adjacent angles that form the

right angle. And therefore, angle 5 and angle 6 are

complementary. supplementary angles add to 180 degrees. So if the angles where adjacent, as we see

here, they would form a straight line. And

therefore are also called, a linear pair. Angle 7 and angle 8 are supplementary angles. The last special pair of angles we’ll take a look at are vertical angles. Vertical angles are two non-adjacent

angles found by intersecting lines. So looking at

this diagram here, notice that angle 1 and angle 2 are adjacent angles. But number 1 and number 3 are non

adjacent angles formed by 2 intersecting lines. So angle 1 and angle 3 are vertical angles. And angle 2 and angle 4 are vertical angle. And all vertical angles are congruent. So angle 1 is congruent to angles 3.

Which means they have the same measure. And there’s a couple ways of indicating 2 angles that have the same measure. 1 way is by the number arcs. So if I

use 1 arcs for angle 1, and 1 art angle 3, we know they

have the same measure. And angle 2 an angle 4 are congruent.

So again, using the arc method I could use 2 arcs for angle 2, and then 2 arcs for angle 4. showing that those 2 angles are

congruent. The other way to show that 2 angles are equal in measure would be to

use hash marks or tick marks. So if I wanna show that angle 1 and angle

3 are congruent, I would put 1 arc for both, and then put 1

hash mark through this arc. And 1 hash mark

through this arc. Showing those 2 angles have the same

measure. And then for angle 2 and angle 4, I would also use one arc. But I have to use 2 hash marks here, and

2 hash marks here, to show that those two angles are equal in

measure. Now let’s go ahead and take a look at some problems, to reinforce these special types of angles. Here we have two intersecting lines and

therefore two pairs of vertical angles. And where asked to determine the measure of each angle. So if we know these 2 angles are

vertical, they must be equal in measure. And we can use this information to

determine the value of X. Since there vertical angles, X plus 16 degrees must equal 4X minus 5 degrees. So we’ll go ahead and solve this for X. subtract X on both sides. So we have 3x minus 5 equals 16. Now I’ll go ahead and add 5 to both

sides. Well if we had 5 to 16, well have 21. Now if we divide both sides by 3, we

know that X must equal 7. So if X is equal to 7, this angle here, would be 7 plus 16 degrees. Or 23

degrees. And therefore because these angles are

vertical angles, this angle here must also be 23 degrees. Which you could verify by subing in

X equals 7 here if we wanted to. Now the remaining 2 angles are also

vertical angles. So this angle here would equal this angle

here. To help us determine the measure of these last two angles, notice that the angles along this line here

would be linear angles and therefore

supplementary. So if this is 23 degrees, and this angle here must be 180 degrees minus 23 degrees. So that’s going to give us 157 degrees. If this angle is 157 degrees and then, so

is this one here. let’s take a look at this last problem

based upon this diagram here. The first question is, name one pair of

vertical angles. So we’re looking for two angles that are

formed by two intersecting lines that are not

adjacent angles. So this angle here would be a vertical

angle with this angle here. So we can say that angle INJ, and angle MNL, are vertical angles. The next question asks, name 1, linear pair of angles. So if we take a look at this line here, the two angles that form this line would

be angle INM. And angle MNL. Notice that the linear pair would also be

supplementary. Next, we want to name two complementary

angles. Remember complementary angles have a sum

of 90 degrees. And since these 2 angles here form a

90 angle, angle INJ and angle JNK, would be complementary. next question, name 2 supplementary

angles. And since we already mentioned a linear pair of these

2 angles here, are supplementary, let’s see if we can find 2 more supplementary

angles. Again, referencing this line here, we

could say that angle INK, an angle KNL are also supplementary, because together they form a straight

angle. And for this last question, it says given that

angle INJ is 61 degrees, find the measure of the following 4

angles. So if angle INJ is 61 degrees, that would be here, let’s see if we can find

the measure of angle JNL. Well angle JNL, and the given angle form a straight angle,

and therefore there supplementary. So angle JNL would be 180 degrees minus 61 degrees. So it would be 119 degrees. Were

asked to determine the measure of angle KNL, which is here. Well notice that angle KNL and angle KNI, are supplementary and form a straight

angle. And angle KNI is 90 degrees . Therefore, angle KNL must also be 90

degrees. And then angle MNL. MNL is here, well it’s a vertical angle with the given angle, therefore, angle MNL must be 61 degrees. Now the last angle is MNI. which is this angle here. Well angle MNI and angle LNM are supplementary. And since we have just said this is 61 degress, angle MNI must be 119 degrees. And the last thing they mentioned here is notice that MNI and angle JNL are vertical angles and

therefore there equal. And we found the measure angle JNL in part A. I think we’ll stop here for

this video. I hope you found this helpful. Thank you for watching.

Homework= Done! Thanks!

um… help me… its my homework actually… <a and <c are complementary <s. if <a = (2x – 10)degrees and <c = (4x – 40)degrees, find <a , <b, <c

Thanks

You are a god. <3

~;♥

Tux needed help

Thank you my Daughter is in the 8th and needed this!!!

Hehehheheheheehe

This is wicked queer

I've been absent for days and the teacher didn't explain me this so thanks you!

You earned yourself a subscriber

Well done!! Amazingly put together. That is the reason for why you just earned another subscriber.

Im learning this in year 6 so to me it is a good head start for secondary school.

your videos are always very helpful. you explain things better than some of the math teachers at my high school.

Thanks!

thanks..

THANKS!!!!!!

boring

SANKU

("'. _ ."')

at 4:55 why did you subtract X?

bro cool

That was defiantly helpfull!

not that good

Thanx u so much for this u help me for the text 2morrow

Stop this nonsense it is the worst video ever

very helpful!only note is i would change the backround color😁💕

Thank you for this vid

Very good video.

Didn't help. Maybe I'm just a dumbass.

Thanks !!!

it is good

bruh i hate math this is not helpful at all loser

idk non of this

Thanks. Helpful pace, and detailed.

Im not really good at maths but this video helped me a lot! thank you and please keep making videos like this! 🙂

This was one of the best explanations I found. I did get thrown off at about 4:47. Why was 5 added to 16? I thought it would be subtracted instead. Can you explain why, please?

Thanks, this was really helpful and understandable now.

Good stuff 🧐🤓👍🏿

thanks this really helped me with my homework

Good video but a little hard to grasp at some parts

3:27 is an answered prayer for me! It is so easy but I could not figure it out on my own. Thank you for providing this educational video!

did you here him at the end

listen closely

Thank you so so much you helpend me a lot I really need more of these lessons!!!

this video was extremely helpful i subed. 🙂

Thank you