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# Worked example: Triangle angles (intersecting lines)

CCSS.Math:

## Video transcript

we're given a bunch of lines here that intersect in all different ways and form triangles and what I want to do in this video we've been given the measures of some of the angles this angle that angle and that angle and what we want to do in this video is figure out what the measure of this angle is and we're going to call that measure X and so I encourage you to pause the video right now and try it yourself and then I'm going to give you the solution so I'm assuming you've unpause it and you V you've solved it or you've give it at least a good shot of it so let's try to do it and what's fun about these is there's multiple ways to solve these and you kind of just have to keep figuring out what you can figure out so let's say you start on the left-hand side right over here if this is 121 degrees then you'd say well look this this angle right over here is supplementary to this angle right over there so this is 121 degrees 121 degrees Plus this green angle has to that has to be equal to 180 degrees so this is going to be 180 180 minus 121 let's see that's the same thing as 80 minus 20 180 minus 20 would be 60 so that's going to be 59 degrees so let me write that down that's going to be 59 59 degrees now we see that we have two angles of a triangle if you have two angles of a triangle you can figure out the third angle because they need to add up to 180 or you could say that this angle right over here so we'll call that question mark we know that 59 plus 29 plus question mark needs to be equal to 180 degrees and if we subtract the 59 the 29 from both sides we get question mark is equal to 180 minus 59 minus 29 degrees so that is going to be 180 minus 59 minus 29 let's see 180 minus 59 we already know is 121 and then 121 minus 29 so if you subtract just 20 you get 101 you subtract another 9 you get 92 so that's going to be equal to 92 degrees this is equal to 92 degrees well if this right here is equal to 92 degrees this angle right here is vertical with that so it is also going to be equal to 92 degrees and now we're getting pretty close we can zoom in on this triangle down here let me save some space here so let me just say that this that over there is also going to be 92 degrees and at this triangle down here we have two of the sides of the triangle we just have to figure out the third and actually we don't have to do much math here because we have one side that's sorry we have two angle we have two of the angles of this triangle we have to figure out the third angle so over here we have one angle that's ninety to one angle is 29 the other one will be 180 minus 92 minus 29 and we don't even have to do any math here because we that's essentially this exact same angles that we have in this triangle right over here we have a 92 degree angle we have a 29 degree angle and the other one is 59 degrees so in this case it has to be also 59 degrees because over here they added up to 180 so over here they'll also add up to 180 so that will also get us to 59 degrees we could just get that by taking 180 subtracting 29 subtracting 92 and then if this is 59 degrees then this angle is also going to be 59 degrees because they are vertical angles so we're done X is equal to X is equal to 59 degrees now there's multiple ways that you could have reason to through this problem you could have immediately said so let me let me let me start over actually maybe a faster way but you wouldn't have been able to do is kind of as basic steps there as you said look this is a this is an exterior angle right over here it is equal to the sum of the remote interior angles so 121 is going to be 29 Plus this thing right over here and we ended up doing that when I did it step by step before but here we're just using kind of a few things that we know about triangles ahead of time to maybe skip a step or two although I like to do it the other way just so we don't make sure we make sure we don't do anything anything weird so anyway this is going to be 129 minus 29 which is going to be 92 and if this is 92 then this is also going to be 92 and then if this is X and this is also going to be X and you could say X plus 92 plus 29 is equal to 100 80 degrees and you would say X plus 92 plus 29 is going to be 121 degrees we already knew that before and so that is going to be that is going to equal 180 degrees and so X is equal to 50 59 X is equal to 59 degrees so there's a ton of ways the ton of ways that you could have you could have thought about thought about this problem