Angles | Worked example

- In the figure above, segment AD is parallel to segment BC. So AD is parallel to BC. So we could put a little parallel symbols right over here. And BE, right over here, is parallel to CD. So these two are parallel to each other. What is the measure of angle ABC? Angle ABC. So that is this angle right over there. Okay, so pause this video and see if you can figure it out on your own before we work through it together. Alright. Now lets do this together. And whenever I have one of these geometry problems where I have to figure out angles, I just like to figure out, well what's everything that I can figure out about this and eventually I will be able to figure out this angle. Or you could take a more strategic approach, but there tends to be multiple ways to do this. So one thing that jumps out at me, because BE is parallel to CD, and you could view segment AD as a transversal, if this angle is 50 degrees, then you have this corresponding angle right over here that is also going to be 50 degrees. Now, if this is 60 degrees, and that is 50 degrees what is this angle going to be? So I'll just do it in this orange color. What's that angle going to be? Well, that angle plus 60 plus 50 needs to add up to 180 degrees. And so that angle is going to be 180 degrees minus 50 degrees minus 60 degrees which is equal to? And in the practice you can use a calculator or you can do this in your head. This is 180 minus 110 so this is going to be 70 degrees. So, we've-we're getting close, we figured out that angle ABE is 70 degrees, but we still have to figure out angle EBC, because if we can figure out this angle right over here, EBC, then we add that to what we just figured out to figure out ABC. Now there, you could use the idea that BC and AD are parallel to each other, and in that world, BE is a transversal. And BE is a transversal between these two parallel lines, then this, this angle right over here, angle CBE and angle AEB, that these are alternate interior angles. And so, when we learn in our geometry about alter interior angles of a transversal that's intersecting two parallel lines, we know that they're going to be equal. So we know that this is going to be equal to 50 degrees. And so angle ABC, which is this thing that I've done in these two blue lines is just going to be the sum of these two. 70 degrees plus 50 degrees is going to be equal to 120 degrees. And we're done.