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Pre-Calculus: Find Angle Complements & Supplements


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About this Lesson

  • Type: Video Tutorial
  • Length: 2:13
  • Media: Video/mp4
  • Use: Watch Online & Download
  • Access Period: Unrestricted
  • Download: MP4 (iPod compatible)
  • Size: 24 MB
  • Posted: 01/22/2009

This lesson is part of the following series:

Trigonometry: Full Course (152 lessons, $148.50)
Pre-Calculus Review (31 lessons, $61.38)
Trigonometry: Trigonometric Functions (28 lessons, $26.73)
Trigonometry: Angles and Radian Measure (5 lessons, $5.94)

This trigonometry lesson introduces and explains the terminology behind complementary angles (angles that add up to 90 degrees) and supplementary angles (that add up to 180 degrees). Professor Burger gives you the definition of these two types of angles, shows you what these angles will look like when combined and and shows you how to find a complement angle or a supplement angle to a provide angle with a known degree measure. Professor Burger will also explain whether supplementary angles and complementary angles could be negative.

Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Precalculus. This course and others are available from Thinkwell, Inc. The full course can be found at: The full course covers angles in degrees and radians, trigonometric functions, trigonometric expressions, trigonometric equations, vectors, complex numbers, and more.

Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".

Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

About this Author

2174 lessons

Founded in 1997, Thinkwell has succeeded in creating "next-generation" textbooks that help students learn and teachers teach. Capitalizing on the power of new technology, Thinkwell products prepare students more effectively for their coursework than any printed textbook can. Thinkwell has assembled a group of talented industry professionals who have shaped the company into the leading provider of technology-based textbooks. For more information about Thinkwell, please visit or visit Thinkwell's Video Lesson Store at

Thinkwell lessons feature a star-studded cast of outstanding university professors: Edward Burger (Pre-Algebra through...


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The Trigonometric Functions
Anglse and Radian Measure
Finding the Complement and Supplement of an Angle Page [1 of 1]
Sometimes we can take a look at two positive angles and ask if they sort of come together and make something nice.
In particular, we say that two positive angles are complimentary. If, in fact, you add up their angle measures, they
equal 90 degrees. So, for example, 45 degrees and 45 degrees, those would be complimentary angles, because if
you add them up, you get 90 degrees. What’s the complimentary angle of 62 degrees? Well, you have to ask
yourself, what angle do you have to write in there in order for this to equal 90? And so, well, that’s just 28 degrees.
What about 93 degrees? What would be the complimentary angle of 93 degrees? Well, I would actually have to write
in here negative 3 degrees. But, complimentary angles must always be positive. So, in fact, this would not have a
complimentary angle. This is too big. Both the angles would have to be less than 90 degrees; otherwise, no good.
So, complimentary angles, both angles must be positive.
Now, what if you take two angles and you add them up and you get 180, that beautiful, sort of pretty straight angle?
Well, then we call those two angles supplementary angles. So, supplementary angles are just any two angles that are
positive that add up to 180 degrees. So, for example, 110 degrees and 70 degrees – those would be, in fact,
supplemental angles, because when you add them up, you get 180. What would be the supplemental angle of 90
degrees? Well, that’s not that hard. It would just be 90 degrees, because, when I add them up, I get 180. How about
170? Well, I would have to figure out what I would have to add to 170 to make it 180. So, it’s just 10 degrees. So,
these two angles are supplemental. These two angles are supplemental. And these two are compliment.
So, sometimes it’s sort of useful to be able to sort of take an angle and sort of write it as the sum, you know, write sort
of one angle plus another angle gives you 90 degrees. That turns out to actually be valuable. So, we have names for
these things. It’s just language here. No new ideas. Just language. Now you know the language.

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