How to Make a 45 Degree Angle Without a Compass

Protractors are accurate and inexpensive tools for drawing angles.

Drawing angles is a skill required in many situations, from school lessons through to working as a cartographer or rocket engineer. Although it is possible to draw many angles with a compass, it is not the only tool available. A semicircular protractor is a useful tool for measuring and drawing angles not exceeding 180 degrees. A protractor has an outer edge marked in degrees, from zero to 180, and a horizontal baseline and vertical centerline to facilitate accurate positioning. Using a protractor is simple.

Things You'll Need

• Protractor
• Pencil

Instructions

1. Draw a horizontal line using the flat base of the protractor. Draw a short vertical line crossing the horizontal one near the left-hand end of the line. This provides a guide for positioning the protractor in Step 2.

2. Rest the protractor over the horizontal line. Ensure that the protractor base line -- joining zero degrees and 180 degrees -- is exactly on top of the line, and that the vertical line in the center of the protractor base aligns with the vertical guideline drawn in Step 1.

3. Locate the 45-degree mark on the curved perimeter of the protractor and make a small pencil mark on the drawing surface.

4. Move the protractor and use the straight base to draw a line between the guide mark on the horizontal line and the mark representing 45 degrees. The angle between the two lines is 45 degrees.

Tips & Warnings

• Use a semicircular protractor to measure any angle between zero and 180 degrees.

• Full circle protractors enable any angle to be drawn.

• Some drafting triangles have 45-degree corners.

• Blunt and wide-tipped pencils reduce the accuracy of measurements. Always use a sharp pencil.

References

• New Mexico State University - College of Arts and Sciences: Angles and Angular Measurement
• OpenLearn: LabSpace: How To Measure an Angle
• Georgia State University Astronomy Program: Angles and Scales
• Math Is Fun: Using a Protractor
• Southern Polytechnic State University Department of Mechanical Engineering Technology ; Chapter 6 Technical Drawing Tools; Simin Nserias
• Washington State University Program in Astronomy; Determination of the Orbit of Mercury; Michael Allen