[Music] in this video we're going to cover how you can use the rules of alternate angles corresponding angles and allied angles importantly though we only use these rules in one specific scenario which is where we have two parallel lines running alongside each other like this and then another line which we can call a transversal cutting through them both whenever this happens we end up with two groups of angles one here at the bottom and another one here at the top and there are four important points that you want to notice about these angles the first is that both groups of angles are both exactly the same for example in this case they both have a 120 degree a 60 degree another 120 degree and another 60 degree angle the second point is that each group only contains two different angles in this case 60 degree angles and 120 degree angles the third point is that the two different angles will always add up to 180 degrees for example here where our angles are 60 degrees and 120 degrees these two add up to 180 degrees and the last point is that vertically opposite angles are always the same for example these two 60 degree angles are considered vertically opposite which is why they're both 60 degrees and likewise these two 120 degree angles are also vertically opposite now as long as you properly understand all of these rules you can use this knowledge to work out unknown angles if one of them is missing for example if we had to find this angle here marked x we'd be able to tell that it's 60 degrees either because it's opposite this 60 degree angle and we know that vertically opposite angles are always equal or because we know that it has to add to this 120 degrees to make 180 to help with more complicated questions though there are three more rules that are worth memorizing the first rule is that alternate angles are the same and what i mean by alternate angles is the two angles found in the corners of a z shape like this for example if we look at our diagram we can see that the z shape is here even though it's been flipped around in this case and so it's these two 60 degree angles that we consider alternate angles the second rule is pretty similar but it says that corresponding angles are the same and corresponding angles are these two angles that you find in an f-shape for example on our diagram the f-shape is here so these two 60-degree angles are corresponding angles the third rule is that allied angles add up to 180 degrees and allied angles are just the interior angles of a c shape so in this diagram these two angles would add together to make 180 degrees we also sometimes call these co-interior angles or just interior angles so just know that allied toe interior and interior all mean the same thing here if you look on our main diagram we can see one of these c shapes here so the allied angles would be this 60 degrees and this 120 degrees which indeed do add together to make 180 one thing to point out with all of these rules is that you'll sometimes see them in other orientations like flipped around in which case they'll be harder to spot but as long as they have the same combination of two parallel lines and one transversal then the rules are going to be the same to see how it all works in practice let's have a go at this exam question so in this question we have a pair of parallel lines a b and c d and then a transversal that cuts through the two of them and we need to find the missing angles x and y now because of all of the different rules that we can use there are normally multiple ways that we can do questions like this and so there's no one correct way of doing it the way i would do it though is notice that this section here is like a backwards c shape and with the 135 degrees and the x are allied or co-interior angles which means that they must add together to make 180 degrees so we now know that 135 plus x equals 180 which means that x is 45 degrees and then because y is vertically opposite x we know that y must be 45 degrees as well anyway that's the end of this video so like always if you want to practice questions on any of this stuff then head over to our platform if you want to go to this particular lesson then click on the link down in the description below or if you want to see our platform in general then click on the link in the top right corner of this screen otherwise we'll see you next time