A 231° angle is a reflex angle: it is bigger than a straight line (180°) but less than a full turn (360°). It is the "outside" of a 129° angle: together they make a full 360° circle.
231° is 77/120 of a full circle, or 77π/60 radians. If you face north and turn 231° clockwise, you end up facing between SW and WSW (closest to southwest (SW)).
231° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 129° |
| Radians | 77π/60 ≈ 4.031711 |
| Gradians | 256.6667 grad |
| Fraction of a turn | 77/120 (64.17%) |
| Degrees, minutes, seconds | 231° 0′ 0″ |
| Compass bearing | between SW and WSW (closest to southwest (SW)) |
Trigonometric values of 231°
| Function | Value |
|---|---|
| sin 231° | −0.777146 |
| cos 231° | −0.62932 |
| tan 231° | 1.234897 |
231° on a protractor
How to draw a 231° angle with a protractor
- Subtract from 360°: 360° − 231° = 129°. A standard protractor only goes to 180°, so you draw the smaller angle first.
- Draw a straight line with a ruler and mark the vertex at one end.
- Place the protractor's center mark on the vertex, line up the 0° baseline with your line, and make a dot at 129°.
- Join the vertex to the dot. The inside angle is 129°; the outside angle, going the long way around, is 231°. Draw the angle arc on the outside and label it 231°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 231° directly.
Drawing it a 231° angle without a protractor (rise and run method)
- 231° = 180° − 51°. Draw a straight line, pick a vertex on it, and build a 51° angle on one side as follows; the angle on the other side of the new line is 129°.
- Draw a straight baseline and measure 8.1 inches (about 8 1/8″) along it from the vertex.
- At that mark, draw a line straight up at 90° and measure exactly 10 inches up it.
- Join the top mark to the vertex. The angle at the vertex is 51°, because tan 51° ≈ 1.2349.
- That gives you 129°. The outside (reflex) angle is 231°.
Where you see 231° angles
- The Earth turns 231° on its axis in about 15 h 24 min.
- A 231° reflex angle is what you measure when you go the "long way" around, like the outside corner of a building or a turn of more than half a circle.
Related angles
231° angle FAQ
What type of angle is 231°?
A 231° angle is a reflex angle, because it is between 180° and 360°.
Does a 231° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 231° is already larger than both. What it does have is an explement (conjugate) of 129°, the angle that completes a full 360° circle.
How many radians is 231 degrees?
231° = 77π/60 radians ≈ 4.0317 rad. To convert degrees to radians, multiply by π/180: 231 × π/180 = 77π/60.
How do I measure a 231° angle on my screen?
Open the online protractor with 231° preset, or type 231 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
