A 159° angle is an obtuse angle: wider than a right angle (90°) but less than a straight line (180°). Its supplement is 21°, so a 159° angle and a 21° angle side by side make a straight line.
159° is 53/120 of a full circle, or 53π/60 radians. If you face north and turn 159° clockwise, you end up facing between SSE and S (closest to south-southeast (SSE)).
159° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 21° |
| Explement (adds to 360°) | 201° |
| Radians | 53π/60 ≈ 2.775074 |
| Gradians | 176.6667 grad |
| Fraction of a turn | 53/120 (44.17%) |
| Degrees, minutes, seconds | 159° 0′ 0″ |
| Compass bearing | between SSE and S (closest to south-southeast (SSE)) |
Trigonometric values of 159°
| Function | Value |
|---|---|
| sin 159° | 0.358368 |
| cos 159° | −0.93358 |
| tan 159° | −0.383864 |
159° on a protractor
How to draw a 159° 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 159° 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 159°.
Drawing it a 159° angle without a protractor (rise and run method)
- 159° = 180° − 21°. Draw a straight line, pick a vertex on it, and build a 21° angle on one side as follows; the angle on the other side of the new line is 159°.
- 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 3.84 inches (about 3 13/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 21°, because tan 21° ≈ 0.3839.
Where you see 159° angles
- The Earth turns 159° on its axis in about 10 h 36 min.
- Obtuse angles like 159° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
159° angle FAQ
What type of angle is 159°?
A 159° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 159°?
The supplement of 159° is 21°, because 159° + 21° = 180°. A 159° angle has no complement, because it is already larger than 90°.
How many radians is 159 degrees?
159° = 53π/60 radians ≈ 2.7751 rad. To convert degrees to radians, multiply by π/180: 159 × π/180 = 53π/60.
How do I measure a 159° angle on my screen?
Open the online protractor with 159° preset, or type 159 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
