{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-26T20:39:41+00:00","modifiedTime":"2016-04-25T19:59:55+00:00","timestamp":"2022-09-14T18:14:26+00:00"},"data":{"breadcrumbs":[{"name":"Business, Careers, & Money","_links":{"self":"https://dummies-api.dummies.com/v2/categories/34224"},"slug":"business-careers-money","categoryId":34224},{"name":"Business","_links":{"self":"https://dummies-api.dummies.com/v2/categories/34225"},"slug":"business","categoryId":34225},{"name":"Accounting","_links":{"self":"https://dummies-api.dummies.com/v2/categories/34226"},"slug":"accounting","categoryId":34226},{"name":"General Accounting","_links":{"self":"https://dummies-api.dummies.com/v2/categories/34230"},"slug":"general-accounting","categoryId":34230}],"title":"Important Angle Measures in Degrees","strippedTitle":"important angle measures in degrees","slug":"important-angle-measures-in-degrees","canonicalUrl":"","seo":{"metaDescription":"When you’re figuring out things like lot lines or fencing for your business, you’re working with angles. These figures are the more commonly used angle measures","noIndex":0,"noFollow":0},"content":"When you’re figuring out things like lot lines or fencing for your business, you’re working with angles. These figures are the more commonly used angle measures and can help you estimate angles for your business tasks:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/251693.image0.jpg\" alt=\"image0.jpg\" width=\"400\" height=\"181\" />","description":"When you’re figuring out things like lot lines or fencing for your business, you’re working with angles. These figures are the more commonly used angle measures and can help you estimate angles for your business tasks:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/251693.image0.jpg\" alt=\"image0.jpg\" width=\"400\" height=\"181\" />","blurb":"","authors":[{"authorId":8985,"name":"Mary Jane Sterling","slug":"mary-jane-sterling","description":" <p><b>Mary Jane Sterling</b> is the author of <i>Algebra I For Dummies, Algebra Workbook For Dummies,</i> and many other <i>For Dummies</i> books. She taught at Bradley University in Peoria, Illinois for more than 30 years, teaching algebra, business calculus, geometry, and finite mathematics. 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She has been teaching at Bradley University, in Peoria, Illinois, for almost 30 of those years.<br> When not teaching or writing, Mary Jane keeps busy by working with her Kiwanis Club, advising Bradley University’s Circle K Club, and working with members of the Heart of Illinois Aktion Club (for adults with disabilities). All the volunteer projects taken on for these clubs help keep her busy and involved in the community.","authors":[{"authorId":34963,"name":"Benjamin Schultz","slug":"benjamin-schultz","description":" <b>Mary Jane Sterling</b> is the author of four other <i>For Dummies</i> titles: <i>Algebra For Dummies, Algebra II For Dummies, Trigonometry For Dummies,</i> and <i>Math Word Problems For Dummies.</i> She has honed her math-explaining skills during her years of teaching mathematics at all levels: junior high school, high school, and college. She has been teaching at Bradley University, in Peoria, Illinois, for almost 30 of those years.<br /> When not teaching or writing, Mary Jane keeps busy by working with her Kiwanis Club, advising Bradley University’s Circle K Club, and working with members of the Heart of Illinois Aktion Club (for adults with disabilities). All the volunteer projects taken on for these clubs help keep her busy and involved in the community.","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/34963"}},{"authorId":8985,"name":"Mary Jane Sterling","slug":"mary-jane-sterling","description":" <p><b>Mary Jane Sterling</b> is the author of <i>Algebra I For Dummies, Algebra Workbook For Dummies,</i> and many other <i>For Dummies</i> books. She taught at Bradley University in Peoria, Illinois for more than 30 years, teaching algebra, business calculus, geometry, and finite mathematics. 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These figures are the more commonly used angle measures and can help you estimate angles for your business tasks:\r\n\r\n","item_vector":null},"titleHighlight":null,"descriptionHighlights":null,"headers":null,"categoryList":["business-careers-money","business","accounting","general-accounting"],"title":"Important Angle Measures in Degrees","slug":"important-angle-measures-in-degrees","articleId":188302},{"objectType":"article","id":190900,"data":{"title":"How to Measure Angles","slug":"how-to-measure-angles","update_time":"2016-03-26T21:05:21+00:00","object_type":"article","image":null,"breadcrumbs":[{"name":"Academics & The Arts","slug":"academics-the-arts","categoryId":33662},{"name":"Math","slug":"math","categoryId":33720},{"name":"Geometry","slug":"geometry","categoryId":33725}],"description":"Measuring angles is pretty simple: the size of an angle is based on how wide the angle is open. Here are some points and mental pictures that will help you to understand how angle measurement works.\nDegree: The basic unit of measure for angles is the degree. \n\nA good way to start thinking about the size and degree-measure of angles is by picturing an entire pizza — that’s 360° of pizza. Cut the pizza into 360 slices, and the angle each slice makes is 1°. For other angle measures, see the following list and figure:\n\n\n If you cut a pizza into four big slices, each slice makes a 90° angle \n\n \n If you cut a pizza into four big slices and then cut each of those slices in half, you get eight pieces, each of which makes a 45° angle \n\n \n If you cut the original pizza into 12 slices, each slice makes a 30° angle \n\n \n\nSo 1/12 of a pizza is 30°, 1/8 is 45°, 1/4 is 90°, and so on. \nThe bigger the fraction of the pizza, the bigger the angle.\n\nThe fraction of the pizza or circle is the only thing that matters when it comes to angle size. The length along the crust and the area of the pizza slice tell you nothing about the size of an angle. In other words, 1/6 of a 10-inch pizza represents the same angle as 1/6 of a 16-inch pizza, and 1/8 of a small pizza has a larger angle (45°) than 1/12 of a big pizza (30°) — even if the 30° slice is the one you’d want if you were hungry. You can see this in the above figure.\nAnother way of looking at angle size is to think about opening a door or a pair of scissors or, say, an alligator’s mouth. The wider the mouth is open, the bigger the angle. As the following figure shows, a baby alligator with its mouth opened wide makes a bigger angle than an adult alligator with its mouth opened less wide, even if there’s a bigger gap at the front of the adult alligator’s mouth.\n\nAn angle’s sides are both rays, and all rays are infinitely long, regardless of how long they look in a figure. The “lengths” of an angle’s sides in a diagram aren’t really lengths at all, and they tell you nothing about the angle’s size. Even when a diagram shows an angle with two segments for sides, the sides are still technically infinitely long rays.\nCongruent angles are angles with the same degree measure. In other words, congruent angles have the same amount of opening at their vertices. If you were to stack two congruent angles on top of each other with their vertices together, the two sides of one angle would align perfectly with the two sides of the other angle.\n\nYou know that two angles are congruent when you know that they both have the same numerical measure (say, they both have a measure of 70°) or when you don’t know their measures but you figure out (or are simply told) that they’re congruent. In figures, angles with the same number of tick marks are congruent to each other, as shown here.","item_vector":null},"titleHighlight":null,"descriptionHighlights":null,"headers":null,"categoryList":["academics-the-arts","math","geometry"],"title":"How to Measure Angles","slug":"how-to-measure-angles","articleId":190900},{"objectType":"article","id":168789,"data":{"title":"What You Need to Know About Angles for Basic Maths Tests","slug":"what-you-need-to-know-about-angles-for-basic-maths-tests","update_time":"2016-04-25T16:11:14+00:00","object_type":"article","image":null,"breadcrumbs":[{"name":"Academics & The Arts","slug":"academics-the-arts","categoryId":33662},{"name":"Math","slug":"math","categoryId":33720},{"name":"Pre-Algebra","slug":"pre-algebra","categoryId":33726}],"description":"Angle is another word for corner. For example, you may hear of footballers scoring from tight angles, meaning they’ve turned the ball round a sharp corner. The word ‘angle’ also shows up in other words, such as ‘triangle’ – which simply means ‘three corners’.\r\n\r\nAngles are measured in degrees. For example, if a car spins 360 degrees, it spins all the way round, while the latitude of London is 53 degrees north of the equator. Confusingly, angle degrees are completely different from temperature degrees – the context usually makes clear which type of degrees you need to work with (except possibly when talking about pointy icicles!). Both types of degree are denoted by a little circle above and after the number, for example: 90º.\r\n\r\nAngles are interesting for many reasons, but one of the key points is that their properties don’t really depend on how big the lines leading to the corner are. For example, the angle on a bookend is the same whether it’s a bookend for tiny books or huge books – in either case, the angle is 90 degrees.\r\nDefining angles\r\nWhen someone says an angle is a certain number of degrees, they’re trying to tell you how sharp the corner is. A small angle means the corner is very sharp, while an angle of 180 degrees isn’t much of an angle at all but instead is a straight line.\r\n\r\nOne degree is defined as ‘one three-hundred-and-sixtieth of a circle’, which isn’t tremendously helpful (but then again, you may not find the technical definitions of metres and kilograms helpful either).\r\nSpecial angles\r\nYou need to know about the following special angles:\r\n\r\n\t\r\n360 degrees is a complete circle. If you turn around 360 degrees, you get back to where you started.\r\n\r\n\t\r\n180 degrees is half a circle. If you turn 180 degrees, you end up facing backwards.\r\n\r\n\t\r\n90 degrees is a quarter-circle, or a right-angle. If you turn 90 degrees, you end up facing to the left or the right of where you started.\r\n\r\n\r\nOther types of angle\r\nYou need to know the following angle-related words:\r\n\r\n\t\r\nAn acute angle is an angle smaller than a right-angle – so less than 90 degrees. Think of ‘acute little puppy’ to remind yourself that it’s a little angle.\r\n\r\n\t\r\nA reflex angle is an angle bigger than 180 degrees. You know when your doctor hits the outside of your knee with a hammer to test your reflexes? Think of that to remember what a reflex angle is: the outside of your knee is always more than 180 degrees.\r\n\r\n\t\r\nAn obtuse angle is in between – so more than 90 degrees but less than 180.\r\n\r\n\r\nMeasuring angles\r\nYou measure angles with a protractor, one of those semi-circular things you had in your pencil case at school.\r\n\r\nHere’s how you measure an angle with a protractor:\r\n\r\n\t\r\nPut the cross-hair in the middle of your protractor over the corner where you want to measure the angle.\r\n\r\n\t\r\nTurn the protractor so that one of the lines going into the angle is on the ‘zero’ line across the bottom of the protractor, to the left of the cross-hair.\r\n\r\n\t\r\nFollow the other line to the edge of the protractor and read the number off the scale – that’s the angle you’re looking for.\r\n\r\n\r\nProtractors are fiddly because they have two different scales running along the same edge and you can easily mix up which one is which. Always use the outside scale – so make sure the zero you use is the zero on the outside track of the protractor.\r\nAfter you measure an angle, look at the angle again and ask whether it makes sense. If you have an angle that’s obviously more than 90 degrees (an obtuse angle) but your protractor says the angle measures 15 degrees, you know something has gone wrong.","item_vector":null},"titleHighlight":null,"descriptionHighlights":null,"headers":null,"categoryList":["academics-the-arts","math","pre-algebra"],"title":"What You Need to Know About Angles for Basic Maths Tests","slug":"what-you-need-to-know-about-angles-for-basic-maths-tests","articleId":168789},{"objectType":"article","id":138789,"data":{"title":"Angles That Form Linear Pairs—Practice Geometry Questions","slug":"angles-that-form-linear-pairspractice-geometry-questions","update_time":"2016-03-26T07:10:45+00:00","object_type":"article","image":null,"breadcrumbs":[{"name":"Academics & The Arts","slug":"academics-the-arts","categoryId":33662},{"name":"Math","slug":"math","categoryId":33720},{"name":"Geometry","slug":"geometry","categoryId":33725}],"description":"Angles that form a linear pair combine to form a straight angle. (A straight angle measures 180 degrees.) The following practice questions ask you to solve problems based on linear pairs. \nPractice questions\nIn the following figure, \n\nat E. In the following questions, fill in the blank to make the statement true.\n\n\n If you know that\n\nare represented by 2a, 2a + b, and 3a – 20, respectively then b = ———?\n \n If you know that\n\n \n\nAnswers and explanations\n\n 20\nStart with the given information:\n\nform a linear pair, which means their sum is 180 degrees. Set up the following equation and solve for a:\n\nPlug in the value of a to find \n\nbecause they’re vertical angles. Set them equal to each other, plug in the value of a, and solve for b:\n\n \n 124 degrees\nAngles that form a linear pair add up to 180 degrees. Set the sum of \n\nequal to 180 and solve for x:\n\nNow plug in the value of x to solve for \n\n \n","item_vector":null},"titleHighlight":null,"descriptionHighlights":null,"headers":null,"categoryList":["academics-the-arts","math","geometry"],"title":"Angles That Form Linear Pairs—Practice Geometry Questions","slug":"angles-that-form-linear-pairspractice-geometry-questions","articleId":138789},{"objectType":"article","id":156839,"data":{"title":"Finding Values for Trigonometry Functions","slug":"finding-values-for-trigonometry-functions","update_time":"2016-03-26T13:14:55+00:00","object_type":"article","image":null,"breadcrumbs":[{"name":"Academics & The Arts","slug":"academics-the-arts","categoryId":33662},{"name":"Math","slug":"math","categoryId":33720},{"name":"Trigonometry","slug":"trigonometry","categoryId":33729}],"description":"You probably know many of the trigonometry functions for the more common angles. Some favorites are:\n\ncos 0° = 1, and tan 45° = 1. That’s three values for three different angles in three different functions. This doesn’t even scratch the surface. Trig functions produce numerical values for all angles, whether in degrees or radians. When you want the secant of an offbeat angle, such as 47 degrees, you need to resort to some resource such as a table of values or a scientific calculator.\nWhere did all these function values come from? Who found them? Are there different formulas to use to find these values? Can they be computed by hand?\nGoing back to the basics of trigonometry, you find a great deal of information from a right triangle. The trig functions can be defined with the measures of the three sides of a right triangle. If you know the measure of an acute angle in a right triangle and you have the measures of the sides, then you can compute the function values with some careful dividing. That’s fine and dandy when you have a 30-60-90 right triangle or a 45-45-90 right triangle. The measures of the sides are\n\nand \n\n(or some multiple of these), respectively. Again, what about that 47-degree angle? If you very carefully construct a right triangle with an angle of 47 degrees, you may be able to get some fairly accurate measurements of the sides and see that this 47-43-90 right triangle has sides measuring about 0.7314-0.6820-1 (or some multiple thereof). How good are you at doing this? Do you trust your calculations?\nActually, trig function values have been around for centuries. In the mid-1500s, the mathematician François Viète created tables of all six functions correct to the nearest minute. Not familiar with the minute measure in trigonometry? Minutes and seconds are used to express fractions of degrees. One degree is equal to 60 minutes and one minute is equal to 60 seconds. So, to express an angle measuring \n\n degrees, you write:\n\n(seven degrees, 30 minutes, 30 seconds). Many cultures and mathematicians dabbled in creating tables of values for the trig functions. You can find tables that give function values to the nearest degree and the nearest minute. Many of the tables have three functions at the head of each column and the respective co-functions of the three functions at the bottom of the same columns. Functions and their co-functions have the same function values, just for different angle measures. This top-and-bottom arrangement saves space in a book.\nBefore handheld calculators, the trig tables found in textbooks or mathematical table publications were the only way to go for the layman. Calculators have made life so much easier. But calculators take some careful attention to details. The first detail, of course, is to have working batteries available. The next detail is to have the calculator set in the correct mode — degrees or radians — depending on what your application is and what form the angles that you’re using are in. When using the calculator to evaluate inverse trig functions, you really need to know about the domain and range of the function to get an accurate reading. The calculator will only tell you what you ask, not necessarily what you need to know.\nWhichever method you use, just be sure to carefully follow any directions and have a working knowledge of the relationships between the different functions.","item_vector":null},"titleHighlight":null,"descriptionHighlights":null,"headers":null,"categoryList":["academics-the-arts","math","trigonometry"],"title":"Finding Values for Trigonometry Functions","slug":"finding-values-for-trigonometry-functions","articleId":156839}]},"relatedArticlesStatus":"success"},"routeState":{"name":"Article4","path":"/article/business-careers-money/business/accounting/general-accounting/important-angle-measures-in-degrees-188302/","hash":"","query":{},"params":{"category1":"business-careers-money","category2":"business","category3":"accounting","category4":"general-accounting","article":"important-angle-measures-in-degrees-188302"},"fullPath":"/article/business-careers-money/business/accounting/general-accounting/important-angle-measures-in-degrees-188302/","meta":{"routeType":"article","breadcrumbInfo":{"suffix":"Articles","baseRoute":"/category/articles"},"prerenderWithAsyncData":true},"from":{"name":null,"path":"/","hash":"","query":{},"params":{},"fullPath":"/","meta":{}}},"dropsState":{"submitEmailResponse":false,"status":"initial"},"sfmcState":{"status":"initial"},"profileState":{"auth":{},"userOptions":{},"status":"success"}}# Important Angle Measures in Degrees

When you’re figuring out things like lot lines or fencing for your business, you’re working with angles. These figures are the more commonly used angle measures and can help you estimate angles for your business tasks: ## About This Article

### This article is from the book:

### About the book authors:

Mary Jane Sterling is the author of four other *For Dummies* titles: *Algebra For Dummies, Algebra II For Dummies, Trigonometry For Dummies,* and *Math Word Problems For Dummies.* She has honed her math-explaining skills during her years of teaching mathematics at all levels: junior high school, high school, and college. She has been teaching at Bradley University, in Peoria, Illinois, for almost 30 of those years.

When not teaching or writing, Mary Jane keeps busy by working with her Kiwanis Club, advising Bradley University’s Circle K Club, and working with members of the Heart of Illinois Aktion Club (for adults with disabilities). All the volunteer projects taken on for these clubs help keep her busy and involved in the community.### This article can be found in the category: