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Basic Shapes #3 Cheat Card: Common Angles

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A circle has 360˚ – we all learned that in school, but we didn’t always learn how to use those 30 dozen degrees to create the angles that make up some of our favorite shapes. Our latest Sew4Home Cheat Card is the third installment in our Basics Shapes trio. It focuses on the most common angles used in sewing and how, with just a trusty protractor and some basic math, you can create your own custom paper piecing shapes, five and six pointed star appliqués, triangles, squares, pentagons, hexagons, octagons, and more. 

To create your own shapes using Common Angles, first set up a base circle as shown on our Cheat Card, in 15˚ increments. We suggest 15˚ rather than the more common 10˚, because 15˚ will allow you to get the more common sewing angles: 30º, 45˚, 60˚, etc. A compass helps you draw a perfect circle. A protractor is required to accurately mark the proper increments. 

The math is simple division. Take your full 360˚ and divide it by the number of points/sides in the shape you want. For example, shown in orange on our Cheat Card is a hexagon, which has six sides. Divide 360˚ by six and you get 60˚. That means the outer points of the hexagon are evenly spaced at every 60˚ around the circle – on our sample at 30˚, 90˚, 150˚, 210˚, 270˚, and 330˚. Connect these points to create your own perfect six-sided shape.

To create a shape with both inner and outer points, such as a star, start in the same manner. For a six-point star, divide 360˚ by six to get 60˚. Divide that result in half to account for the inner points, which results in 30˚. The points of your star will advance in 30˚ increments around the circle, alternating by inner and outer points. On our sample, shown below in red, we start at 0˚ with the first inner point, followed by the first outer point at 30˚, then continue in that manner around the circle: inner at 60˚, outer at 90˚, inner at 120˚, outer at 150˚, inner at 180˚, outer at 210˚, inner at 240˚, outer at 270˚, inner at 300˚, outer at 330˚, and that brings you back around to your start. For a five-point star, you simply divide 360˚ by 5, which equals 72˚. Divide that in half to get 36˚. Your inner and outer points will be 36˚ apart. The depth of the inner points is determined by the size of your inner circle, which can be whatever size you’d like.

Just like Leonardo da Vinci’s famous Vitruvian Man, now you know the secret of the angles and shapes within a perfect 360˚ circle.

All of our Cheat Cards are the size of a standard business card: 2” wide x 3½” high. That’s small enough to tuck into your wallet or tack up on the bulletin board in your sewing room. This mini size makes them super convenient, but of course, we can’t possibly fit every bit of information onto them, which is why we’ve given you some additional math formula information above.

The Basic Shapes #3 Cheat Card is available in six different backgrounds. All six designs print out on one 8½” x 11” sheet of paper from which you can cut out the cards. You may want to print on a heavier card stock (80 to 100 lb cover is a good option) or print on regular paper then glue that lighter weight sheet to a stiff backing material prior to cutting. There are crop marks on each card to help you get a perfect slice.

This is the sixth installment in our Cheat Card series and rounds out the available cards for 2017. You may also want to print out the Yardage Conversion Cheat Cards, Measuring Tape Cheat Cards, Sewing Machine Needles Cheat Cards, Basic Shapes #1 Cheat Card: The Circle, and Basic Shapes #2 Cheat Card: Common Straight Line Shapes. These five sets of cards are set-up on the same variety of backgrounds. Pick your favorite design and build a set, or cut them all out to share.

We’ve also found it handy to laminate the cut cards, punch a hole in one upper corner of each, and clip one or more cards onto a key ring or carabiner.

In the new year, we’ll be putting Cheat Card Sets into our Sew4HomeShop on Etsy. We’ll collect all six Cards onto one printable page, offering a full set of six in each of the six pretty backgrounds. We'll announce on the site as soon as these are available. 

The Basic Shapes #3 Cheat Card: Common Angles is available here as a .PDF file. Click the image below to download. You will need Adobe Acrobat Reader DC, which is a free program.

We’ve minimized the file size, but please be patient with the download process. In addition, make sure you have the latest version of Acrobat Reader DC, and the latest version of your printer driver. Adobe does always recommend a re-start of your computer with any update.

If you are experiencing printing issues, you can also try the Print as Image option in your printer’s browser window. This option is often under the Advanced tab. You can also save the downloaded PDF to your computer and print from there.

Is there a cheat or hack you wish you could have as a handy mini card? Leave us a comment below and we’ll add it to our list.

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Comments (6)

M D-B said:
M D-B's picture

I was a straight A student until my sophomore year when I met geometry. I had zero understanding of what they were trying to teach me.The nuns were  kind to let me switch out of the class to take sewing instead. That switch led to a life time of sewing and I did learn some basic geometry to boot! A win-win.

Liz Johnson.Editor.Sew4Home said:
Liz Johnson.Editor.Sew4Home's picture

M D-B - Thanks so much for that story... it's an important one, and we certainly agree that more "real life" teaching would be so much better for so many.

Momo said:
Momo's picture

I took geometry and did very well in it; the only math class I ever enjoyed.  I learned little in practical terms, nor did I use it in everyday life, until I decided to learn to sew really well.  Pi became a tool for me, finally, after 30 years, and that was nearly 30 years ago!  And I learned how to make a flounce instead of a ruffle, and so many other things!  Sewing taught me so much that never made much sense in school!  What a terrible shame it is so seldom taught, if at all, in schools anymore.  If the math teacher worked with the home Ec teacher, we'd have all been better taught.  Not just in sewing, but cooking, too.  Thank you, S4H for helping to fill in the gaps for lots of us!    

Liz Johnson.Editor.Sew4Home said:
Liz Johnson.Editor.Sew4Home's picture

@Momo - Thanks - I think your sentiments are similar to many folks out there. Yes, we may have learned this sometime in the past, but having it summarized and related to a real-life use can make all the difference. 

Becky Campbell said:
Becky Campbell's picture

So helpful. Theses will so fill the void of the Geomety class I did no time take in high school. 

Liz Johnson.Editor.Sew4Home said:
Liz Johnson.Editor.Sew4Home's picture

@Becky - You are so welcome. Even in geometry class, these helpful tips weren't necessarily taught. You now have new, mad skills!