At 268°, this is a reflex angle, which goes more than halfway around a circle. It is the "outside" of a 92° angle: together they make a full 360° circle.
268° is 67/90 of a full circle, or 67π/45 radians. If you face north and turn 268° clockwise, you end up facing between WSW and W (closest to west (W)).
268° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 92° |
| Radians | 67π/45 ≈ 4.677482 |
| Gradians | 297.7778 grad |
| Fraction of a turn | 67/90 (74.44%) |
| Degrees, minutes, seconds | 268° 0′ 0″ |
| Compass bearing | between WSW and W (closest to west (W)) |
Trigonometric values of 268°
| Function | Value |
|---|---|
| sin 268° | −0.999391 |
| cos 268° | −0.034899 |
| tan 268° | 28.636253 |
268° on a protractor
How to draw a 268° angle with a protractor
- Subtract from 360°: 360° − 268° = 92°. 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 92°.
- Join the vertex to the dot. The inside angle is 92°; the outside angle, going the long way around, is 268°. Draw the angle arc on the outside and label it 268°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 268° directly.
Drawing it a 268° angle without a protractor (rise and run method)
- 268° = 180° − 88°. Draw a straight line, pick a vertex on it, and build an 88° angle on one side as follows; the angle on the other side of the new line is 92°.
- Draw a straight baseline and measure 0.35 inches (about 3/8″) 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 88°, because tan 88° ≈ 28.6363.
- That gives you 92°. The outside (reflex) angle is 268°.
Where you see 268° angles
- The Earth turns 268° on its axis in about 17 h 52 min.
- A 268° 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
268° angle FAQ
What type of angle is 268°?
A 268° angle is a reflex angle, because it is between 180° and 360°.
Does a 268° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 268° is already larger than both. What it does have is an explement (conjugate) of 92°, the angle that completes a full 360° circle.
How many radians is 268 degrees?
268° = 67π/45 radians ≈ 4.6775 rad. To convert degrees to radians, multiply by π/180: 268 × π/180 = 67π/45.
How do I measure a 268° angle on my screen?
Open the online protractor with 268° preset, or type 268 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
