[Music] welcome to math with mr j [Music] in this video i'm going to cover 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 0 minus 5 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 five plus five is ten so we have a zero here carry the one one plus six is seven plus two is nine so those two angles equal ninety 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 zero minus two let's borrow we have ten minus two which is eight and then eight minus seven one 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 you have it there's an explanation of complementary angles remember two angles that add up to 90 degrees and then how we go about finding a missing complementary angle i hope that helped thanks so much for watching until next time peace