At 106°, this is an obtuse angle, opened up past a square corner but not yet flat. Its supplement is 74°, so a 106° angle and a 74° angle side by side make a straight line.
106° is 53/180 of a full circle, or 53π/90 radians. If you face north and turn 106° clockwise, you end up facing between E and ESE (closest to east-southeast (ESE)).
106° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 74° |
| Explement (adds to 360°) | 254° |
| Radians | 53π/90 ≈ 1.850049 |
| Gradians | 117.7778 grad |
| Fraction of a turn | 53/180 (29.44%) |
| Degrees, minutes, seconds | 106° 0′ 0″ |
| Compass bearing | between E and ESE (closest to east-southeast (ESE)) |
Trigonometric values of 106°
| Function | Value |
|---|---|
| sin 106° | 0.961262 |
| cos 106° | −0.275637 |
| tan 106° | −3.487414 |
106° on a protractor
How to draw a 106° 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 106° 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 106°.
Drawing it a 106° angle without a protractor (rise and run method)
- 106° = 180° − 74°. Draw a straight line, pick a vertex on it, and build a 74° angle on one side as follows; the angle on the other side of the new line is 106°.
- Draw a straight baseline and measure 2.87 inches (about 2 7/8″) along it from the vertex.
- At that mark, draw a line straight up at 90° and measure exactly 10 inches up it.
- Join the top mark to the vertex. The angle at the vertex is 74°, because tan 74° ≈ 3.4874.
Where you see 106° angles
- The Earth turns 106° on its axis in about 7 h 4 min.
- Obtuse angles like 106° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
106° angle FAQ
What type of angle is 106°?
A 106° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 106°?
The supplement of 106° is 74°, because 106° + 74° = 180°. A 106° angle has no complement, because it is already larger than 90°.
How many radians is 106 degrees?
106° = 53π/90 radians ≈ 1.85 rad. To convert degrees to radians, multiply by π/180: 106 × π/180 = 53π/90.
How do I measure a 106° angle on my screen?
Open the online protractor with 106° preset, or type 106 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
