![]() The measure of an angle is important in classifying angles, as we’re about to see. If we wrote this out, we would write it like this: If we were to place one on our trusty angle we would find that it measures 45 degrees: Speaking of measuring, remember the protractor? We use it to measure angles. Sometimes you’ll see lowercase letters instead of numbers or Greek symbols like \(\theta\) or \(\alpha\). But most of the time we like to use letters to name our angles, since the numbers could be confused with the measure of an angle. Since most of us have three names, it’s only fair that angles have a bunch too. We can now call it ∠1 or we can call it ∠ABC or we can call it ∠B. Now we have an additional name for this angle. Sometimes angles will be labeled with numbers inside the arc, like this: So it’s important to be precise when dealing with more than one angle. In this case, we’d have to call the angles by their long names, because point B is the vertex of ∠ABC, ∠DBC, and ∠DBA! If we asked someone to just look at ∠B they wouldn’t know which of these we meant. Be careful though, because sometimes a single point can be the vertex of multiple angles, like this: In this case, we could also call this angle B. If the point that is the vertex is only a part of one angle then we can use a shorter name. We can actually call this ∠CBA and it is just as correct. Here, B is the vertex so the B goes between the A and the C. When naming angles with three letters, the vertex point must be in the middle. Now we can refer to our angle as angle ABC (∠ABC). Here’s our simple angle again but with a few points added on the rays: Sometimes we have many angles, so in order to tell them apart, we have a system for naming them. We usually see vertices whenever lines meet or in polygons like triangles and quadrilaterals. We’ve also created a vertex, which is the point where the two rays meet. If we take this ray and add another ray to it that has the same endpoint, we’ve created an angle. A ray is a line with a single endpoint that extends infinitely in one direction. Hope this video was helpful.Hi, and welcome to this video about angles Supplementary are two angles that add to one hundred and eighty so sixty and one twenty are supplements of each other. Forty and fifty are complements so they are complementary angles. Here is our example forty plus fifty is ninety. Complementary are two angles that ad to ninety. So let’s look at the rules for supplementary and complementary angles. I take one eighty and I subtract sixty five and I’m left with one fifteen, so my angle is one hundred and fifteen degrees. So if this angle is sixty five what is this unknown angle? Well supplementary. So when you draw an angle off of that line you will have two angles that are supplements of each other. This is a straight line and straight lines have an angle of one hundred and eighty degrees. Now let’s look at an application problem of that concept. So one hundred and five and seventy five are supplementary to each other. We will take X plus our one hundred and five and set it to one hundred and eighty subtract one hundred and five from both sides so X is seventy five degrees. So a hundred and five degrees is the supplement of what angle. So it is very similar, complementary is ninety, supplementary is one eighty. The definition for supplementary angles is two angles that add to one eighty. So that makes this angle twenty two so sixty eight and twenty two are complements of each other. ![]() So if I know one angle is sixty eight I can subtract it from ninety and I get twenty two degrees. In a right triangle the two acute angles are complementary. OK now let’s look at of an application of complementary. So I will subtract thirty from both sides and I get sixty. Thirty is the complement of what angle? Well the definition says “Take thirty minus the unknown angle and it will add up to ninety. The definition of complementary angle is two angles that add to 90. This little symbol ∠ is the symbol for angles just so you will recognize the symbol.
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