A 267° 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 93° angle: together they make a full 360° circle.
267° is 89/120 of a full circle, or 89π/60 radians. If you face north and turn 267° clockwise, you end up facing between WSW and W (closest to west (W)).
267° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 93° |
| Radians | 89π/60 ≈ 4.660029 |
| Gradians | 296.6667 grad |
| Fraction of a turn | 89/120 (74.17%) |
| Degrees, minutes, seconds | 267° 0′ 0″ |
| Compass bearing | between WSW and W (closest to west (W)) |
Trigonometric values of 267°
| Function | Value |
|---|---|
| sin 267° | −0.99863 |
| cos 267° | −0.052336 |
| tan 267° | 19.081137 |
267° on a protractor
How to draw a 267° angle with a protractor
- Subtract from 360°: 360° − 267° = 93°. 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 93°.
- Join the vertex to the dot. The inside angle is 93°; the outside angle, going the long way around, is 267°. Draw the angle arc on the outside and label it 267°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 267° directly.
Drawing it a 267° angle without a protractor (rise and run method)
- 267° = 180° − 87°. Draw a straight line, pick a vertex on it, and build an 87° angle on one side as follows; the angle on the other side of the new line is 93°.
- Draw a straight baseline and measure 0.52 inches (about 1/2″) 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 87°, because tan 87° ≈ 19.0811.
- That gives you 93°. The outside (reflex) angle is 267°.
Where you see 267° angles
- The Earth turns 267° on its axis in about 17 h 48 min.
- A 267° 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
267° angle FAQ
What type of angle is 267°?
A 267° angle is a reflex angle, because it is between 180° and 360°.
Does a 267° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 267° is already larger than both. What it does have is an explement (conjugate) of 93°, the angle that completes a full 360° circle.
How many radians is 267 degrees?
267° = 89π/60 radians ≈ 4.66 rad. To convert degrees to radians, multiply by π/180: 267 × π/180 = 89π/60.
How do I measure a 267° angle on my screen?
Open the online protractor with 267° preset, or type 267 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
