here we have an angle what is the name of the angle one way to name it is angle ABC the letter B is in the middle of the name because the angle is at B we can also name it angle B because there is only one angle at B but what happens if we have the line BD to the diagram we now have two angles at B angle abd and angle DBC in this case we cannot just use B for the name there is however another option if we number the angles angle abd we can now name angle b1 and angle DBC we can name angle B to please pause to study this notation whenever we have angles next to each other we call them adjacent angles here is another example of adjacent angles and here is another example adjacent angles always share a common vertex here the vertex is Ed B and they also share one side or arm of the angles please pause to study this here we have two lines a B and C D which intersect at 90 degrees we know that it is 90 degrees because this is the symbol we use for a right angle whenever lines intersect at 90 degrees we call them perpendicular lines in maths we can write this in shorthand as follows this means that a B is perpendicular to C D please pause if you need to here we again have a right angle if I now add a line to the sketch and I tell you that angle q1 is 30 degrees of angle q2b it will be 90 degrees minus 30 degrees why because we are told that the whole like you is 90 degrees angle q2 is therefore equal to 60 degrees this means that if we add these two angles the answer will be 90 degrees whenever angles add up to 90 degrees we say that they are complementary angles so remember complementary angles add up to 90 degrees please pause if you need to here we are asked to find the complement of 42 degrees in other words we need to find a second angle so that 42 degrees and the second angle are complementary angles to find this compliment we simply subtract 42 degrees from 90 degrees the complement of 42° is therefore 48 degrees please pause and find the complement of 28° to find it we again subtract the given angle from 90 degrees the compliment is therefore 62° were you correct what do you think the complement of X will be it is simply 90 degrees minus X is this what you said what do you think the compliment of 90 degrees minus a will be as before we subtract the given angle from 90 degrees I use brackets in the step to show that we are subtracting the whole given angle next we need to multiply the minus into the bracket this is equal to 90 degrees minus 90 degrees plus a the compliment is therefore a please pause to check my working here is the next question please pause to read it we are given that this whole angle is 90 degrees we can therefore say that the sum of these angles is 90 degrees and the reason is they are complementary angles we then add 12 degrees and 28 degrees to get X plus 40 degrees on the left X is therefore equal to 50 degrees please pause to check my working here is a similar question please pause and try it on your own first we can again state the two given angles add up to 90 degrees and the reason is there are complementary angles next we add like terms on the left we then isolate the term with X by subtracting 15 degrees from both sides and to isolate X we divide both sides by 3 please pause to check my working do you remember what the size of a straight angle or straight line is it is 180 degrees this is a very important fact to remember in mathematics if I now add the line Q s to the sketch we get to adjacent angles angle Q 1 and angle Q 2 if angle q1 equals 125 degrees what will the sizeof angle q2 be to find this angle we subtract 125 degrees from 180 degrees angle q2 is therefore equal to 55 degrees this means that if we add these two angles we will get an answer of 180 degrees whenever angles add up to 180 degrees we say that they are supplementary angles so remember supplementary angles add up to 180 degrees please pause if you need to here we are asked to find the supplement of 42 degrees in other words we need to find a second angle so that 42 degrees and the second angle are supplementary angles to answer this we need to subtract the given angle from 180 degrees the supplement of 42° is therefore 138° next we are asked to find the supplement of 128 degrees please pause to do it we again subtract the given angle from 180 degrees the supplement is there 452 degrees how did you do what do you think the supplement of X will be as before we subtract the given angle from 180 degrees were you correct and what about the supplement 90 degrees minus a to find it we again subtract the given angle from 180 degrees and we need to use brackets to show that we are subtracting the whole given angle next we need to multiply the minus into the bracket this is equal to 180 degrees minus 90 degrees plus a the supplement is there for 90 degrees plus a please pause to check my working here is the next question please pause to read it because PQR is a straight line we can state that the sum of the angles is 180 degrees and the reason is straight line or we can now also use the reason supplementary angles both are correct - 30 degrees plus 70 degrees equals 40 degrees giving us X plus 40 degrees on the left X is therefore equal to 140 degrees please pause to check my working here is a similar question please pause to try it on your own first because we have adjacent angles on a straight line we can write the following and the reason is supplementary angles next we add like terms on left giving us 6x equals 180 degrees we then divide both side by 6:00 to get the answer please pause to check my working here is the next question please pause to read it this right angle symbol tells us that we have a 90-degree angle in the middle and because we again have adjacent angles on a straight line we can write the following and the reason is supplementary angles we then add like terms on the left giving us 3x plus 81 degrees equals 180 degrees to isolate the term with X we subtract 81 degrees from both sides and to isolate X we divide both sides by 3 please force to check my working let's end with this question please pause to read it we are asked to find X which is this angle in the triangle but where do we start we need to start with a straight line can you see how we can say that the three adjacent angles add up to 180 degrees why because they are supplementary angles 58 degrees plus 71 degrees equals 129 degrees so on the Left we have angle c2 plus 129 degrees Anglesey - is therefore equal to 51 degrees we are now ready to work inside the triangle can you see how it is an isosceles triangle so this angle is also 51 degrees we can therefore state that X plus 51 degrees plus 51 degrees equals 180 degrees why because the angles of a triangle always add up to 180 degrees fifty-one degrees plus 51 degrees equals 102 degrees so on the Left we have X plus 102 degrees we then isolate X by subtracting 102 degrees from both sides this completes the lesson good luck with the test