A 285° 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 75° angle: together they make a full 360° circle.
285° is 19/24 of a full circle, or 19π/12 radians. If you face north and turn 285° clockwise, you end up facing between W and WNW (closest to west-northwest (WNW)).
285° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 75° |
| Radians | 19π/12 ≈ 4.974188 |
| Gradians | 316.6667 grad |
| Fraction of a turn | 19/24 (79.17%) |
| Degrees, minutes, seconds | 285° 0′ 0″ |
| Compass bearing | between W and WNW (closest to west-northwest (WNW)) |
Trigonometric values of 285°
| Function | Value |
|---|---|
| sin 285° | −(√6 + √2)/4 ≈ −0.965926 |
| cos 285° | (√6 − √2)/4 ≈ 0.258819 |
| tan 285° | −(2 + √3) ≈ −3.732051 |
285° on a protractor
How to draw a 285° angle with a protractor
- Subtract from 360°: 360° − 285° = 75°. 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 75°.
- Join the vertex to the dot. The inside angle is 75°; the outside angle, going the long way around, is 285°. Draw the angle arc on the outside and label it 285°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 285° directly.
Drawing it a 285° 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).
- Inside it, starting from the second arm, mark a 15° angle: construct a 30° angle, then bisect it.
- What is left between the first arm and the new line is 90° − 15° = 75°.
- That gives you 75°. The reflex angle on the outside of it is 285°.
Where you see 285° angles
- The Earth turns 285° on its axis in about 19 hours.
- A 285° 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
285° angle FAQ
What type of angle is 285°?
A 285° angle is a reflex angle, because it is between 180° and 360°.
Does a 285° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 285° is already larger than both. What it does have is an explement (conjugate) of 75°, the angle that completes a full 360° circle.
How many radians is 285 degrees?
285° = 19π/12 radians ≈ 4.9742 rad. To convert degrees to radians, multiply by π/180: 285 × π/180 = 19π/12.
How do I measure a 285° angle on my screen?
Open the online protractor with 285° preset, or type 285 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
