A 288° 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 72° angle: together they make a full 360° circle.
288° is 4/5 of a full circle, or 8π/5 radians. The minute hand of a clock sweeps 288° in 48 minutes. If you face north and turn 288° clockwise, you end up facing between W and WNW (closest to west-northwest (WNW)).
288° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 72° |
| Radians | 8π/5 ≈ 5.026548 |
| Gradians | 320 grad |
| Fraction of a turn | 4/5 (80%) |
| Degrees, minutes, seconds | 288° 0′ 0″ |
| Compass bearing | between W and WNW (closest to west-northwest (WNW)) |
Trigonometric values of 288°
| Function | Value |
|---|---|
| sin 288° | −√(10 + 2√5)/4 ≈ −0.951057 |
| cos 288° | (√5 − 1)/4 ≈ 0.309017 |
| tan 288° | −3.077684 |
288° on a protractor
How to draw a 288° angle with a protractor
- Subtract from 360°: 360° − 288° = 72°. 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 72°.
- Join the vertex to the dot. The inside angle is 72°; the outside angle, going the long way around, is 288°. Draw the angle arc on the outside and label it 288°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 288° directly.
Drawing it a 288° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 3.25 inches (about 3 1/4″) 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 72°, because tan 72° ≈ 3.0777.
- That gives you 72°. The outside (reflex) angle is 288°.
Where you see 288° angles
- The Earth turns 288° on its axis in about 19 h 12 min.
- A 288° 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
288° angle FAQ
What type of angle is 288°?
A 288° angle is a reflex angle, because it is between 180° and 360°.
Does a 288° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 288° is already larger than both. What it does have is an explement (conjugate) of 72°, the angle that completes a full 360° circle.
How many radians is 288 degrees?
288° = 8π/5 radians ≈ 5.0265 rad. To convert degrees to radians, multiply by π/180: 288 × π/180 = 8π/5.
How do I measure a 288° angle on my screen?
Open the online protractor with 288° preset, or type 288 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
