Complementary and Supplementary Angles | How to Find Missing Angles | Math with Mr. J

[Music] welcome to math with mr j [Music] in this video i'm going to cover both complementary and supplementary angles let's start with complementary angles now complementary angles are two angles that add up to 90 degrees so if the sum of two angles is 90 degrees they are complementary let's jump into our examples where we have complementary angles but one of the angles will be unknown or missing and we need to find that missing angle measure for number one we are given an angle measure of 25 degrees right here so angle w x z equals 25 degrees we need to figure out the angle measure of angle z x y now we know that the two angles are complementary they will equal 90 degrees so we have 25 degrees plus what will give us that 90 degrees now you may be able to think through this and figure it out using mental math and think well 25 degrees plus what equals 90 degrees well 25 plus 65 so our missing angle measure is going to be 65 degrees angle zxy equals 65 degrees if you can figure these out mentally that works for sure but if not that's fine too what we can do we can take the 90 degrees that we know these two angles are going to add up to so let's write 90 degrees and we can subtract the angle measure that we are given so 90 degrees minus 25 degrees now we're ready to subtract so we have zero minus five we need to borrow let's borrow from the 9 here and we have 10 minus 5 which is 5 and then 8 minus 2 is 6. so we get 65 degrees that way as well again 90 degrees because we know the two angles are going to add up to 90 degrees and we can subtract the given angle measure in order to get that missing angle measure we can also check to see if our answer is correct by adding our two angles and then seeing if it equals 90 degrees so let's double check here we can do 65 degrees plus 25 degrees if that equals 90 then we're good to go 5 plus 5 is 10 so we have a 0 here carry the 1 1 plus 6 is 7 plus 2 is 9. so those two angles equal 90 we have the correct answer there the missing angle there is 65 degrees let's try another example here and move on to number two where we have a given angle measure of 72 degrees so angle g f h equals 72 degrees we need to figure out angle h f e so let's do 90 degrees we have complementary angles here so we know they are going to equal 90 and we are going to subtract the given angle measure now again if you can figure this out mentally that's great that works but if not that's fine too we can always write out a subtraction problem to find that angle so we have 0-2 let's borrow we have 10 minus 2 which is 8 and then 8 minus 7 1. so our missing angle angle hfe is going to be 18 degrees let's double check to make sure so we'll do 72 degrees plus 18 degrees make sure it equals 90. 2 plus 8 is 10 so let's put our 0 carry the 1 and then 1 plus 7 is 8 plus 1 is 9. so those two angles do in fact equal 90 we have the correct angle measure for hfe 18 degrees so there's an explanation of complementary angles let's move on to supplementary angles now supplementary angles are two angles that add up to 180 degrees and a 180 degree angle is going to make a straight line so if the sum of two angles is 180 degrees they are supplementary let's jump into our examples where we have supplementary angles but one of the angles will be unknown or missing and we need to find that missing angle measure for number one we have a given angle measure of 65 degrees so angle d b c equals 65 degrees so we need to find the missing or unknown angle we are going to look for angle a b d now we know that the sum of these two angles is going to be 180 degrees they are supplementary angles so we need to think we have 65 degrees and then we need to add what to get to 180 degrees if you can figure these out mentally that works for sure but if not that's fine too so what we can do we can take the sum of these two angles which we know is going to be 180 degrees so we will write 180 degrees and we'll subtract the angle measure that we are given 65 degrees that's going to give us our missing angle so let's subtract 0 minus 5 well we need to borrow 10 minus 5 is 5 7 minus 6 is 1 and then we have a 1 in the hundreds place so 115 degrees and that is angle a b d 115 degrees we can always double check our work and make sure that that angle measure is correct and we do this by adding 115 degrees plus the 65 degrees and make sure they equal 180 we'll start with 5 plus 5 which is 10 we'll put our 0 here carry the one plus one is two plus six is eight and then we have a one in the hundreds place so 180 degrees 115 degrees was correct and we are good to go let's move on to number two where we have a given angle measure of 124 degrees so that's for angle t s u so with that given angle we need to find the angle measure of angle r s u let's calculate what that missing or unknown angle measure is by taking 180 degrees and subtracting our given angle measure of 124 degrees so we'll start with 0 minus 4 we need to borrow so we have ten minus four which is six seven minus two is five and then one minus one is zero so we have 56 degrees angle rsu equals 56 degrees and again we can always double check let's do that so we can add 124 degrees plus 56 degrees and make sure that equals 180 degrees 4 plus 6 gives us 10 carry the 1. 1 plus 2 is 3 plus 5 8 and then we have a 1 in the hundreds place so 180 degrees 56 degrees was correct for angle rsu so there you have it there's an explanation of both complementary and supplementary angles and how to find missing complementary and supplementary angles i hope that helped thanks so much for watching until next time peace