A 255° 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 105° angle: together they make a full 360° circle.
255° is 17/24 of a full circle, or 17π/12 radians. If you face north and turn 255° clockwise, you end up facing between WSW and W (closest to west-southwest (WSW)).
255° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 105° |
| Radians | 17π/12 ≈ 4.45059 |
| Gradians | 283.3333 grad |
| Fraction of a turn | 17/24 (70.83%) |
| Degrees, minutes, seconds | 255° 0′ 0″ |
| Compass bearing | between WSW and W (closest to west-southwest (WSW)) |
Trigonometric values of 255°
| Function | Value |
|---|---|
| sin 255° | −(√6 + √2)/4 ≈ −0.965926 |
| cos 255° | −(√6 − √2)/4 ≈ −0.258819 |
| tan 255° | 2 + √3 ≈ 3.732051 |
255° on a protractor
How to draw a 255° angle with a protractor
- Subtract from 360°: 360° − 255° = 105°. 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 105°.
- Join the vertex to the dot. The inside angle is 105°; the outside angle, going the long way around, is 255°. Draw the angle arc on the outside and label it 255°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 255° directly.
Drawing it a 255° angle without a protractor (compass and ruler)
- Draw a 90° angle: construct a perpendicular line (draw arcs from two points on the line and join their crossing points).
- Using the second arm as your new base, add a 15° angle on the outside: construct a 30° angle, then bisect it.
- The angle between the first arm and the new arm is 90° + 15° = 105°.
- That gives you 105°. The reflex angle on the outside of it is 255°.
Where you see 255° angles
- The Earth turns 255° on its axis in about 17 hours.
- A 255° 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
255° angle FAQ
What type of angle is 255°?
A 255° angle is a reflex angle, because it is between 180° and 360°.
Does a 255° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 255° is already larger than both. What it does have is an explement (conjugate) of 105°, the angle that completes a full 360° circle.
How many radians is 255 degrees?
255° = 17π/12 radians ≈ 4.4506 rad. To convert degrees to radians, multiply by π/180: 255 × π/180 = 17π/12.
How do I measure a 255° angle on my screen?
Open the online protractor with 255° preset, or type 255 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
