A 20° angle is classed as acute because it measures less than 90°. It is less than half of a right angle, and its complement (the angle that makes 90° with it) is 70°.
20° is one eighteenth (1/18) of a full circle, or π/9 radians. If you face north and turn 20° clockwise, you end up facing between N and NNE (closest to north-northeast (NNE)).
20° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 70° |
| Supplement (adds to 180°) | 160° |
| Explement (adds to 360°) | 340° |
| Radians | π/9 ≈ 0.349066 |
| Gradians | 22.2222 grad |
| Fraction of a turn | one eighteenth (1/18) (5.56%) |
| Degrees, minutes, seconds | 20° 0′ 0″ |
| Slope (grade) | 36.4% |
| Roof pitch | 4.37/12 |
| Compass bearing | between N and NNE (closest to north-northeast (NNE)) |
Trigonometric values of 20°
| Function | Value |
|---|---|
| sin 20° | 0.34202 |
| cos 20° | 0.939693 |
| tan 20° | 0.36397 |
20° on a protractor
How to draw a 20° angle with a protractor
- Draw a straight line with a ruler. This is the first arm; mark the vertex at one end.
- Place the center mark of the protractor exactly on the vertex and line up the 0° baseline with your line.
- Find 20° on the row of numbers that reads 0° on your line (protractors have two rows running in opposite directions) and make a small dot at the edge.
- Remove the protractor and draw a line from the vertex through the dot. Mark the angle with an arc and label it 20°.
Drawing it a 20° angle without a protractor (rise and run method)
- Draw a straight baseline and measure exactly 10 inches along it from the vertex.
- At the 10-inch mark, draw a short line straight up at 90° (use a carpenter's square or the corner of a sheet of paper).
- Measure 3.64 inches (about 3 5/8″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 20°, because tan 20° ≈ 0.364.
Where you see 20° angles
- Most Western (German-style) kitchen knives are sharpened at about 20° per side.
- Divide a circle into 18 equal slices and each slice is 20°, e.g. 18 spokes on a wheel or 18 equal pie-chart wedges.
- A 9-sided frame (nonagon) is assembled with 20° miter cuts.
- A board sloped at 20° rises about 43.7 inches over a 10-foot (120-inch) run.
- 20° of latitude on Earth spans roughly 1,381 miles north to south.
- The Earth turns 20° on its axis in about 1 h 20 min.
Related angles
20° angle FAQ
What type of angle is 20°?
A 20° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 20°?
The complement of 20° is 70° (together they make 90°), and the supplement is 160° (together they make 180°).
How many radians is 20 degrees?
20° = π/9 radians ≈ 0.3491 rad. To convert degrees to radians, multiply by π/180: 20 × π/180 = π/9.
What is 20° as a slope or roof pitch?
20° is a 36.4% slope, which is a roof pitch of 4.37/12 (a rise of about 4 3/8 inches for every 12 inches of run).
