Learn about Angle Addition and Bisection In this lesson, let’s learn about the angle addition postulate and we’ll also figure out how to deal with bisection of angles. Bisection means dividing the angles into two equal parts. So, the angle addition postulate essentially says that if I have an angle that says ABC and I have a line that lies within that angle well, let’s call it D then, the sum of these two smaller angles, ABD and DBC. The measure of these two when added equals to the measure of the entire angle. It would visually make sense because these two small angles ultimately are equal to the bigger angle anyway because the bigger angle is the same as the sum of the two smaller ones. But, let’s use that in real life. We are given that measure of angle ABD, this big angle is 84 degrees. The measure of angle ABC, this angle, is 42 degrees. This is 84 degrees. We need to find this one. Well, the addition postulate says, this plus this would equal to this or addition postulate says the measurement of ABC plus the measure of DBC equals the measure of ABD. Substituting the values, 42 degrees plus the measure of DBC equals 84 degrees. Subtracting 42 degrees from both sides, I get the measure of DBC equals 42 degrees. 84 minus 42 is 42. So, what am I given? The measure of this angle is 42 degrees as well which means these two are congruent angles. I can mark them with a single dash that cuts through them which means they are of the same size. Let’s do a slightly difficult problem and it tells us about bisection. It says the ray BC bisects angle ABD. Bisects means this and this are equal. And we are told that measure of DBC which is this angle is 6x+3. The measure of ABC or CBA is 8x - 7. We need to find this. How do we do this? Well, to find this I need to find the two individual angles and I can add them. What am I given? This angle is 6x+3. This angle is 8x - 7 but I know they are equal. So, 6x plus 3 equals 8x minus 7. These two angles are equal, right? So, if I subtract 6x from both sides, what do I get? Well, three equals 2x-7. Now, let’s add 7 to both sides so I get 10 equals 2x or x equals 5. so, if x equals 5, what is this angle. It’s 6 times 5 plus 3 is 33 degrees. Here, 8 times 5 is 40 minus 7 is 33 degrees. So if both these smaller angles are 33, what’s the bigger angle, it’s the sum of this two, right? So, the measure of angle ABD should be 33 degrees plus 33 degrees equals 66 degrees. Key thing to remember, when an angle is bisected, the two angles are equal. The two angles formed are equal.