A 278° angle is reflex because it measures between 180° and 360°. It is the "outside" of an 82° angle: together they make a full 360° circle.
278° is 139/180 of a full circle, or 139π/90 radians. If you face north and turn 278° clockwise, you end up facing between W and WNW (closest to west (W)).
278° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 82° |
| Radians | 139π/90 ≈ 4.852015 |
| Gradians | 308.8889 grad |
| Fraction of a turn | 139/180 (77.22%) |
| Degrees, minutes, seconds | 278° 0′ 0″ |
| Compass bearing | between W and WNW (closest to west (W)) |
Trigonometric values of 278°
| Function | Value |
|---|---|
| sin 278° | −0.990268 |
| cos 278° | 0.139173 |
| tan 278° | −7.11537 |
278° on a protractor
How to draw a 278° angle with a protractor
- Subtract from 360°: 360° − 278° = 82°. 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 82°.
- Join the vertex to the dot. The inside angle is 82°; the outside angle, going the long way around, is 278°. Draw the angle arc on the outside and label it 278°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 278° directly.
Drawing it a 278° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 1.41 inches (about 1 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 82°, because tan 82° ≈ 7.1154.
- That gives you 82°. The outside (reflex) angle is 278°.
Where you see 278° angles
- The Earth turns 278° on its axis in about 18 h 32 min.
- A 278° 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
278° angle FAQ
What type of angle is 278°?
A 278° angle is a reflex angle, because it is between 180° and 360°.
Does a 278° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 278° is already larger than both. What it does have is an explement (conjugate) of 82°, the angle that completes a full 360° circle.
How many radians is 278 degrees?
278° = 139π/90 radians ≈ 4.852 rad. To convert degrees to radians, multiply by π/180: 278 × π/180 = 139π/90.
How do I measure a 278° angle on my screen?
Open the online protractor with 278° preset, or type 278 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
