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It Depends on the Angle - How to Distinguish between Complimentary and Supplementary Angles

My Basic Algebra Concepts class always does a brief chapter on geometry...my favorite to teach! We usually spend time working on angles and their definitions. My students always have difficulty distinguishing complimentary from supplementary angles. Since most of my students are visual learners, I had to come up with something that would help them to distinguish between the two.

The definition states that complementary angles are any two angles whose sum is 90°. (The angles do not have to be next to each other to be complementary.) As seen in the diagram on the left, a 30° angle + a 60° angle = 90° so they are complementary angles. Notice that the two angles form a right angle or 1/4 of a circle.

If I write the word complementary and change the first letter "C" into the number nine and I think of the letter "O" as the number zero, I have a memory trick my mathematical brain can remember.


Supplementary Angles are two angles whose sum is 180°. Again, the two angles do not have to be together to be supplementary, just so long as the total is 180 degrees. In the illustration on your right, a 110° angle + a 70° angle = 180°; so, they are supplementary angles. Together, they form a straight angle or 1/2 of a circle.

If I write the word supplementary and alter the "S" so it looks like an 8, I can mentally imagine 180°.


Since there are so many puns for geometric terms. I have to share a bit of geometry humor. (My students endure many geometry jokes!)



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You might be interested in a variety of hands-on ideas on how to introduce angles to your students. Check out Having Fun With Angles.  It explains how to construct different kinds of angles (acute, obtuse, right, straight) using items such as coffee filters, plastic plates, and your fingers. Each item or manipulative is inexpensive, easy to make, and simple for students to use. All of the activities are hands-on and work well for kinesthetic, logical, spatial, and/or visual learners.

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7 comments:

Socrates Lantern said...

Thanks so much for sharing this helpful information. Great title too.

Kathie @Tried and True Teaching Tools said...

I love this, Vicky! I didn't realize complementary angles did not need to be next to each other! I'm going to use these visuals for 90 and 180. Thanks!! I'm sure you must algebra so fun and understandable for your students!

marcy said...

I love tricks like this. I need to use them and I know there are many students out there who just need that extra something to get it to stick.

Simple Steps to Sentence Sense by Charlene Tess said...

Very clever ideas to help students remember. You must be a great math teacher!

Margo Gentile said...

Very creative! The associations you show your students will certainly help them to remember which angle is which. I like the way you use different manipulatives to demonstrate angles.

Teaching Ideas For Those Who Love Teaching said...

Nice post and very informative! Thank you for sharing!

Retta said...

Love these ideas! Especially the one about complimentary angles! Thanks for bringing this one back!