At 166°, this is an obtuse angle, opened up past a square corner but not yet flat. Its supplement is 14°, so a 166° angle and a 14° angle side by side make a straight line.
166° is 83/180 of a full circle, or 83π/90 radians. If you face north and turn 166° clockwise, you end up facing between SSE and S (closest to south-southeast (SSE)).
166° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 14° |
| Explement (adds to 360°) | 194° |
| Radians | 83π/90 ≈ 2.897247 |
| Gradians | 184.4444 grad |
| Fraction of a turn | 83/180 (46.11%) |
| Degrees, minutes, seconds | 166° 0′ 0″ |
| Compass bearing | between SSE and S (closest to south-southeast (SSE)) |
Trigonometric values of 166°
| Function | Value |
|---|---|
| sin 166° | 0.241922 |
| cos 166° | −0.970296 |
| tan 166° | −0.249328 |
166° on a protractor
How to draw a 166° 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 166° 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 166°.
Drawing it a 166° angle without a protractor (rise and run method)
- 166° = 180° − 14°. Draw a straight line, pick a vertex on it, and build a 14° angle on one side as follows; the angle on the other side of the new line is 166°.
- 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 2.49 inches (about 2 1/2″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 14°, because tan 14° ≈ 0.2493.
Where you see 166° angles
- The Earth turns 166° on its axis in about 11 h 4 min.
- Obtuse angles like 166° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
166° angle FAQ
What type of angle is 166°?
A 166° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 166°?
The supplement of 166° is 14°, because 166° + 14° = 180°. A 166° angle has no complement, because it is already larger than 90°.
How many radians is 166 degrees?
166° = 83π/90 radians ≈ 2.8972 rad. To convert degrees to radians, multiply by π/180: 166 × π/180 = 83π/90.
How do I measure a 166° angle on my screen?
Open the online protractor with 166° preset, or type 166 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
