How to Measure 45 Degrees on a Circle
A full circle measures 360 degrees. An angle of 45 degrees is equivalent to 1/8 of a full circle, or half of a right angle. Two simple ways to measure a 45-degree angle are to use a protractor or use the circumference of the circle. Both methods assume knowledge of the location of the center of the circle. Both methods require only basic math skills. A calculator is required.
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Instructions
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Measuring by Angle
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1
Place the protractor in the center of the circle, with the central mark - a small circle or vertical line on the middle of the protractor base - directly over the center of the circle.
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2
Mark two points on the outside edge of the protractor that are 45 degrees apart. For example, make a mark next to zero degrees and another next to 45 degrees.
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3
Remove the protractor. Draw a radius line from the center point, through the first mark, to the edge of the circle. Draw a second radius from the center point, through the second mark, to the edge of the circle. The angle between the lines is 45 degrees.
Measuring by Circumference Length
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4
Measure the circumference of the circle. Be as precise as possible. Record the distance as a decimal value, using either metric units or decimal feet. This permits division of the values with a calculator.
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5
Divide the circumference by eight. Forty-five degrees is 1/8 of a circle, so an angle of 45 degrees produces an arc 1/8 of the length of the circle's circumference. Record this value.
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6
Mark a point on the circle circumference. Measure, around the circumference, the distance found in Step 2, and then make a second mark. Draw a straight line from each mark to the center of the circle. The angle between the two lines is 45 degrees.
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Tips & Warnings
Use a protractor when the protractor and circle are of similar sizes. Use the second method when a protractor is not available or the circle is much larger than the protractor.
Using a sharp pencil point reduces errors.
Using a protractor in the center of a relatively large circle introduces errors. Compared to the distance to the edge of the circle, the angle guide on the protractor is small. The lines drawn may go off course without the error being obvious.
References
- City University of New York - Borough of Manhattan Community College; Angles and Their Measurement; Lawrence Spector
- National Security Agency: What's Your Angle - Classifying And Measuring Angles
- South Kitsap School District: How to Construct Circle Graphs
- University of Minnesota; Arc Length Conjecture; David Wiggins
- University of Akron - Department of Theoretical and Applied Mathematics; Introduction To Angles; Thomas E. Price
Resources
- Photo Credit Stockbyte/Stockbyte/Getty Images
