Protractors are tools used in mathematics to measure the width of angles in degrees. You might need one for a homework assignment or construction project, so it's worth learning how to make it. You can use a printable template or create it by folding a sheet of paper to always have the tool available.
Steps
Method 1 of 3: Print a Protractor on Paper
Step 1. Get a sheet of thick or clear paper
Find cardboard or other similar material that fits into the printer to make a stronger protractor. if you opt for transparent paper, the tool is easier to use.
Read the printer instructions before proceeding to make sure you can use transparent paper
Step 2. Download a printable template
Search online and find a protractor template that you can download.
For better print quality, choose a large image. The sharpness of the lines depends on the size of the file; look for something that is at least 540x620
Step 3. Print the image
Use the printer to transfer the diagram to paper; look at the print preview to make sure the whole protractor is printed on the sheet.
Change the size of the template according to your needs. In general, the straight side of the instrument should be between 8 and 15 cm long for best results
Step 4. Cut out the protractor
Use a pair of scissors to cut along the edges of the image; remember to also remove the inner portion of the arch.
Step 5. Rest the bottom edge on one of the sides that define the corner
Align the straight portion of the protractor with one of the two sides of the angle you want to measure; the point where the second side intersects the arc of the instrument defines the amplitude of the angle itself.
Method 2 of 3: Building a Pocket Protractor
Step 1. Cut out a square from a sheet of paper
Take a regular A4 sheet and reduce it to a square.
- Use a ruler to measure a 21cm long segment along the 30cm side and make a mark at this point.
- Use a ruler to draw a straight cross line that starts right from the mark you made.
- Cut out the paper exactly along this line; you should get a square of 21 cm on each side.
Step 2. Fold the paper in half
Bring the left side of the square over the right and define the crease in the center; then open the square.
- Line up the edges perfectly to make sure the crease is right in the center.
- The accuracy of the corners depends on the quality and accuracy of the folds.
Step 3. Fold the top right corner into a triangle
Take this corner and bring it towards the lower point of the fold you made earlier in the center of the square; make the edge of the corner line up with the center crease.
- The angle should occupy approximately 2/3 of the medial crease.
- This operation allows you to create a triangle with an angle of 30 °, one of 60 ° and one of 90 °.
- You can fold the entire top edge down to create a new tip on the top left corner.
Step 4. Fold the bottom right corner up and make a second triangle
Bring the apex to the edge of the first triangle until the right side of the paper lines up with it.
This way, you get a second triangle with angles of 30 °, 60 ° and 90 °
Step 5. Fold the bottom left corner up
Always take the vertex and bring it up until the left side of the paper lines up with the edge of the first triangle you made at the top. The two edges should match perfectly.
Tuck the tip of the corner under the second 30 °, 60 °, and 90 ° triangle you folded
Step 6. Write the amplitudes of the angles of your protractor
The side of each triangle you made defines an angle of different width that you should label. Place the paper on a table with the long side facing up.
- There are two angles at the top of the instrument: the one on the left is 15 °, while the one on the right is 30 °.
- On the left there are two angles: the upper one measures 45 ° and the lower one 30 °.
- The right angle of the protractor is 60 °.
- The one defined on the right side of the instrument, at the point where there is a line that crosses it, measures 90 °.
- The lower left corner has a width of 45 ° (right) and 30 ° (left).
Step 7. Use the pocket protractor
You can use it to evaluate the angles of different amplitudes by supporting the corresponding vertex.
- Evaluate the width of the angles that do not coincide with those on the protractor.
- You can further divide the corners into smaller triangles by folding them in half.
Step 8. Place the protractor on the angle you are trying to estimate
Rotate it to find the one that lines up perfectly with the sides of the object in question.
Determine the amplitude of the angle you are measuring by pairing it with the various angles available to you on the protractor
Method 3 of 3: Draw a Protractor
Step 1. Use a ruler to draw a horizontal line
Draw a 12 cm long segment on a sheet of paper; alternatively, you can use the edge of the paper itself as the underside of the tool and skip this step.
Draw a mark in the center of the line so that it is exactly 6 cm from each end
Step 2. Draw a half circle with a compass
Use this tool to connect the two ends of the line with an arc.
- Set the compass so that it draws a half circle with a diameter of 12 cm.
- Draw a semicircle that joins the ends of the horizontal line or is centered at the midpoint of the edge of the paper.
Step 3. Fold a square piece of paper to create precise width corners
Fold it exactly in half lengthwise and diagonally.
- A sheet of origami paper is suitable for this purpose.
- You can cut out a perfect square by folding the top edge of a regular A4 sheet and aligning it with the side edge. Draw a line along the underside that crosses the sheet horizontally and cut off the underside of the sheet.
- Use a fully open square to draw the 90 ° angle on the protractor. Rest the base of the square on the lower edge of the tool; align the height with the medial point of the protractor and draw a line along the edge of the square.
Step 4. Mark the corners on the protractor
By folding a square in half you get an angle of 45 °. Lay the triangle obtained along the edge of the protractor and draw a notch at the point where the side of the triangle intersects the arc; label this notch with "45 °".
- Make a triangle by bringing one edge of the upper left corner of the paper towards the center, thus obtaining an angle of 60 °. Reproduce the same fold on the right side to obtain an angle of 120 ° and report these amplitudes on the protractor. Remember that every time you fold a triangle you create a pair of complementary angles for both sides of the protractor.
- Fold a new triangle by bringing the inside edge of the triangle extending from the top left corner to the center of the paper. The vertex of the triangle should be slightly to the right of the median line of the paper itself and you should see an imaginary line extending from the corner to the center; this line defines an angle of 75 ° and one of 105 °.
- Turn the folded sheet and place the edge on the right angle of the protractor; at this point the edge of the triangle defines angles of 15 ° and 165 °.
Step 5. Cut out the protractor
Use a pair of scissors to carefully follow the outer edge of the semicircle.
Make a small "D" in the center of the tool to see the lines of the angles you want to measure
Step 6. Measure the angles
Align the bottom edge of the protractor with one of the sides of the angle you want to estimate; look at the point where the other side intersects the protractor arc to determine the amplitude.
Place the vertex of the corner in the center of the straight edge of the tool
Advice
- Wait for the ink to dry completely on the clear sheet before cutting out the protractor; if you go too early, the color may smudge.
- To get exact measurements, make precise and well-defined folds when making the pocket protractor.
- You can bring larger angles back to the pocket protractor by opening the folds and doubling the width.
- Block the triangles you folded by putting adhesive tape in the center; in this way the protractor keeps its shape.
