A 168° angle is an obtuse angle: wider than a right angle (90°) but less than a straight line (180°). Its supplement is 12°, so a 168° angle and a 12° angle side by side make a straight line.
168° is 7/15 of a full circle, or 14π/15 radians. The minute hand of a clock sweeps 168° in 28 minutes. If you face north and turn 168° clockwise, you end up facing between SSE and S (closest to south-southeast (SSE)).
168° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 12° |
| Explement (adds to 360°) | 192° |
| Radians | 14π/15 ≈ 2.932153 |
| Gradians | 186.6667 grad |
| Fraction of a turn | 7/15 (46.67%) |
| Degrees, minutes, seconds | 168° 0′ 0″ |
| Compass bearing | between SSE and S (closest to south-southeast (SSE)) |
Trigonometric values of 168°
| Function | Value |
|---|---|
| sin 168° | 0.207912 |
| cos 168° | −0.978148 |
| tan 168° | −0.212557 |
168° on a protractor
How to draw a 168° 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 168° 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 168°.
Drawing it a 168° angle without a protractor (rise and run method)
- 168° = 180° − 12°. Draw a straight line, pick a vertex on it, and build a 12° angle on one side as follows; the angle on the other side of the new line is 168°.
- 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 2.13 inches (about 2 1/8″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 12°, because tan 12° ≈ 0.2126.
Where you see 168° angles
- Each interior corner of a regular 30-sided polygon measures 168°.
- The Earth turns 168° on its axis in about 11 h 12 min.
- Obtuse angles like 168° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
168° angle FAQ
What type of angle is 168°?
A 168° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 168°?
The supplement of 168° is 12°, because 168° + 12° = 180°. A 168° angle has no complement, because it is already larger than 90°.
How many radians is 168 degrees?
168° = 14π/15 radians ≈ 2.9322 rad. To convert degrees to radians, multiply by π/180: 168 × π/180 = 14π/15.
How do I measure a 168° angle on my screen?
Open the online protractor with 168° preset, or type 168 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
