A 264° 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 96° angle: together they make a full 360° circle.
264° is 11/15 of a full circle, or 22π/15 radians. The minute hand of a clock sweeps 264° in 44 minutes. If you face north and turn 264° clockwise, you end up facing between WSW and W (closest to west (W)).
264° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 96° |
| Radians | 22π/15 ≈ 4.607669 |
| Gradians | 293.3333 grad |
| Fraction of a turn | 11/15 (73.33%) |
| Degrees, minutes, seconds | 264° 0′ 0″ |
| Compass bearing | between WSW and W (closest to west (W)) |
Trigonometric values of 264°
| Function | Value |
|---|---|
| sin 264° | −0.994522 |
| cos 264° | −0.104528 |
| tan 264° | 9.514364 |
264° on a protractor
How to draw a 264° angle with a protractor
- Subtract from 360°: 360° − 264° = 96°. 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 96°.
- Join the vertex to the dot. The inside angle is 96°; the outside angle, going the long way around, is 264°. Draw the angle arc on the outside and label it 264°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 264° directly.
Drawing it a 264° angle without a protractor (rise and run method)
- 264° = 180° − 84°. Draw a straight line, pick a vertex on it, and build an 84° angle on one side as follows; the angle on the other side of the new line is 96°.
- Draw a straight baseline and measure 1.05 inches (about 1 1/16″) 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 84°, because tan 84° ≈ 9.5144.
- That gives you 96°. The outside (reflex) angle is 264°.
Where you see 264° angles
- The Earth turns 264° on its axis in about 17 h 36 min.
- A 264° 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
264° angle FAQ
What type of angle is 264°?
A 264° angle is a reflex angle, because it is between 180° and 360°.
Does a 264° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 264° is already larger than both. What it does have is an explement (conjugate) of 96°, the angle that completes a full 360° circle.
How many radians is 264 degrees?
264° = 22π/15 radians ≈ 4.6077 rad. To convert degrees to radians, multiply by π/180: 264 × π/180 = 22π/15.
How do I measure a 264° angle on my screen?
Open the online protractor with 264° preset, or type 264 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
