A 156° angle is an obtuse angle: wider than a right angle (90°) but less than a straight line (180°). Its supplement is 24°, so a 156° angle and a 24° angle side by side make a straight line.
156° is 13/30 of a full circle, or 13π/15 radians. The minute hand of a clock sweeps 156° in 26 minutes. If you face north and turn 156° clockwise, you end up facing between SE and SSE (closest to south-southeast (SSE)).
156° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 24° |
| Explement (adds to 360°) | 204° |
| Radians | 13π/15 ≈ 2.722714 |
| Gradians | 173.3333 grad |
| Fraction of a turn | 13/30 (43.33%) |
| Degrees, minutes, seconds | 156° 0′ 0″ |
| Compass bearing | between SE and SSE (closest to south-southeast (SSE)) |
Trigonometric values of 156°
| Function | Value |
|---|---|
| sin 156° | 0.406737 |
| cos 156° | −0.913545 |
| tan 156° | −0.445229 |
156° on a protractor
How to draw a 156° 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 156° 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 156°.
Drawing it a 156° angle without a protractor (rise and run method)
- 156° = 180° − 24°. Draw a straight line, pick a vertex on it, and build a 24° angle on one side as follows; the angle on the other side of the new line is 156°.
- 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 4.45 inches (about 4 7/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 24°, because tan 24° ≈ 0.4452.
Where you see 156° angles
- Each interior corner of a regular 15-sided polygon measures 156°.
- The Earth turns 156° on its axis in about 10 h 24 min.
- Obtuse angles like 156° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
156° angle FAQ
What type of angle is 156°?
A 156° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 156°?
The supplement of 156° is 24°, because 156° + 24° = 180°. A 156° angle has no complement, because it is already larger than 90°.
How many radians is 156 degrees?
156° = 13π/15 radians ≈ 2.7227 rad. To convert degrees to radians, multiply by π/180: 156 × π/180 = 13π/15.
How do I measure a 156° angle on my screen?
Open the online protractor with 156° preset, or type 156 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
