A 167° angle is obtuse because it is greater than 90° and less than 180°. Its supplement is 13°, so a 167° angle and a 13° angle side by side make a straight line.
167° is 167/360 of a full circle, or 167π/180 radians. If you face north and turn 167° clockwise, you end up facing between SSE and S (closest to south-southeast (SSE)).
167° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 13° |
| Explement (adds to 360°) | 193° |
| Radians | 167π/180 ≈ 2.9147 |
| Gradians | 185.5556 grad |
| Fraction of a turn | 167/360 (46.39%) |
| Degrees, minutes, seconds | 167° 0′ 0″ |
| Compass bearing | between SSE and S (closest to south-southeast (SSE)) |
Trigonometric values of 167°
| Function | Value |
|---|---|
| sin 167° | 0.224951 |
| cos 167° | −0.97437 |
| tan 167° | −0.230868 |
167° on a protractor
How to draw a 167° 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 167° 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 167°.
Drawing it a 167° angle without a protractor (rise and run method)
- 167° = 180° − 13°. Draw a straight line, pick a vertex on it, and build a 13° angle on one side as follows; the angle on the other side of the new line is 167°.
- 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 2.31 inches (about 2 5/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 13°, because tan 13° ≈ 0.2309.
Where you see 167° angles
- The Earth turns 167° on its axis in about 11 h 8 min.
- Obtuse angles like 167° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
167° angle FAQ
What type of angle is 167°?
A 167° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 167°?
The supplement of 167° is 13°, because 167° + 13° = 180°. A 167° angle has no complement, because it is already larger than 90°.
How many radians is 167 degrees?
167° = 167π/180 radians ≈ 2.9147 rad. To convert degrees to radians, multiply by π/180: 167 × π/180 = 167π/180.
How do I measure a 167° angle on my screen?
Open the online protractor with 167° preset, or type 167 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
