A 164° angle is obtuse because it is greater than 90° and less than 180°. Its supplement is 16°, so a 164° angle and a 16° angle side by side make a straight line.
164° is 41/90 of a full circle, or 41π/45 radians. If you face north and turn 164° clockwise, you end up facing between SSE and S (closest to south-southeast (SSE)).
164° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 16° |
| Explement (adds to 360°) | 196° |
| Radians | 41π/45 ≈ 2.86234 |
| Gradians | 182.2222 grad |
| Fraction of a turn | 41/90 (45.56%) |
| Degrees, minutes, seconds | 164° 0′ 0″ |
| Compass bearing | between SSE and S (closest to south-southeast (SSE)) |
Trigonometric values of 164°
| Function | Value |
|---|---|
| sin 164° | 0.275637 |
| cos 164° | −0.961262 |
| tan 164° | −0.286745 |
164° on a protractor
How to draw a 164° 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 164° 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 164°.
Drawing it a 164° angle without a protractor (rise and run method)
- 164° = 180° − 16°. Draw a straight line, pick a vertex on it, and build a 16° angle on one side as follows; the angle on the other side of the new line is 164°.
- 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 2.87 inches (about 2 7/8″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 16°, because tan 16° ≈ 0.2867.
Where you see 164° angles
- The Earth turns 164° on its axis in about 10 h 56 min.
- Obtuse angles like 164° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
164° angle FAQ
What type of angle is 164°?
A 164° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 164°?
The supplement of 164° is 16°, because 164° + 16° = 180°. A 164° angle has no complement, because it is already larger than 90°.
How many radians is 164 degrees?
164° = 41π/45 radians ≈ 2.8623 rad. To convert degrees to radians, multiply by π/180: 164 × π/180 = 41π/45.
How do I measure a 164° angle on my screen?
Open the online protractor with 164° preset, or type 164 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
