TenMarks teaches you how angle pairs formed by parallel lines
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Learn about Angle Pairs Formed by Parallel Lines In this lesson, let’s learn more about parallel lines and what it does two pairs of angles or angle pairs. So we’re given a figure like K and L, this is K, this is line L a parallel lines which are cut by a transversal t right here. And we see in red the eight angles that we’re talking about. We’re given angle four as 60 degrees, this angle is 60 degrees. We need to find the angles two, three, six and eight so two, three, six and eight. These are what we need to find. So here’s what I’m going to do. We know this angle is 60 degrees, this measurement we know. So there is something called a corresponding angle postulate. So vertical angles or corresponding angles are always congruent. congruent means they’re equal. So vertical angles which are angles that are not adjacent across from each other are congruent. Vertical or corresponding angles are congruent. When they’re congruent which means angle four equals angle two. So what is angle two? That’s 60 degrees as well so we’ve figured out angle two. Now, let’s look at if we know angle two and this is 60 degrees—let me change the color of my pen—if these are adjacent angles you see this angle two and angle three are adjacent and they both lay in the same lines. So adjacent angles which fall on the same line and those are the only two angles are complimentary. So angle two plus angle three will be 180 degrees. 180 degrees because this is a straight line so if this is 60 this is bound to be 120 degrees, right? There are other ways of doing that as well but this is the easy way, 60 and 120, a straight line is always 180 degrees, right? Now, angle six is an alternate exterior angle to angle four. Notice that this is the interior, this is the exterior so alternate exterior angles are congruent as well. What is that mean? Alternate exterior are angle four equals angle six. So if I know angle four is 60 degrees, angle six is also 60 degrees so I’ve got that. Now, since six is 60, six and eight are vertical angles so angle six equals angle eight which is 60 degrees as well. So in this case, angle eight is also 60 degrees. So we’ve found all four angles by simply knowing one of them. The key thing to remember and you can see this visually as well. Let me erase all the markings—I’m just trying to walk you through something a little simple. As we can see, this is a straight line so one and four will always total a 180 degrees. Just remember that opposite angles are always equal and adjacent angles are always total of 180 if they both line the straight line. So if we just know this and we know that alternate angles, etcetera we can figure out the rest. Visually, you can see that this angle and this angle look about the same. The key thing to remember is anytime two parallel lines are intersected by a transversal. Any angles will either be congruent or will total 180 degrees there’s no other way out. The angles five and six, five and seven, five and eight, five and three will either be equal or they will be a sum of 180 degrees, there’s no third option.