TenMarks teaches you about adjacent angles and linear pairs.
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Learn about Angle Pairs In this lesson, let’s learn about angle pairs and we have to tell whether the angles given to us are adjacent, adjacent and from a linear pair or not adjacent at all. So, before we go down the path of figuring the three out, let’s learn what we mean by each one of these. So when we have two angles, let’s say this is one angle and this is another angle. Let’s say this is A, B, C, and D. So, what’s an angle? An angle is two rays, BC and BD with a common vertex, B. Similarly, AB and AC are common rays or two rays that form the angle with a common vertex B. So when these two angles share a common ray, if these two angles share a common ray, angle ABC and angle CBD. Since they share a common ray C, they are called adjacent angles. If the two adjacent angles, let’s say it was like this, if this was how it looked and this angle and this angle are still adjacent, ABC is adjacent to CBD, but BD and BA are opposite rays, exactly in the opposite direction then these two angles are called a linear pair. Linear pair, the bigger angle is always a straight line which is 180 degrees. So, let’s use these two things to solve what we’re given. We have to tell whether the angles are adjacent, linear pair, or not adjacent at all. First is number one and number three, number one and number three. Well, number one is UPT and this number three is TPS. Do they share a common ray? Yes, they do. This is the common ray that they share. So, they share a common ray. They are adjacent but the other two rays that are not shared. Are they forming a straight line? No, they are not. They are not opposing or opposite rays so they are not a linear pair. Let’s look at the next one. Number three and RPQ. Number three is this one and RPQ is this one, RPQ. Well, these two don’t have common rays. The rays forming number three are SP and PT and here it’s RP and PQ. One, two rays, three rays, four rays, they don’t share a common ray. So, these angles are not adjacent. Let’s look at the third one, number one and number two. Number one is this one. Number two is this one. Well, they share a common ray which is PU. PU is the common ray and the other two rays which is this one and this one, PT and PQ are opposite rays. They form a straight line. This is a straight line. So, this is adjacent but also are linear pair.