At 310°, this is a reflex angle, which goes more than halfway around a circle. It is the "outside" of a 50° angle: together they make a full 360° circle.
310° is 31/36 of a full circle, or 31π/18 radians. If you face north and turn 310° clockwise, you end up facing between WNW and NW (closest to northwest (NW)).
310° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 50° |
| Radians | 31π/18 ≈ 5.410521 |
| Gradians | 344.4444 grad |
| Fraction of a turn | 31/36 (86.11%) |
| Degrees, minutes, seconds | 310° 0′ 0″ |
| Compass bearing | between WNW and NW (closest to northwest (NW)) |
Trigonometric values of 310°
| Function | Value |
|---|---|
| sin 310° | −0.766044 |
| cos 310° | 0.642788 |
| tan 310° | −1.191754 |
310° on a protractor
How to draw a 310° angle with a protractor
- Subtract from 360°: 360° − 310° = 50°. 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 50°.
- Join the vertex to the dot. The inside angle is 50°; the outside angle, going the long way around, is 310°. Draw the angle arc on the outside and label it 310°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 310° directly.
Drawing it a 310° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 8.39 inches (about 8 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 50°, because tan 50° ≈ 1.1918.
- That gives you 50°. The outside (reflex) angle is 310°.
Where you see 310° angles
- The Earth turns 310° on its axis in about 20 h 40 min.
- A 310° 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
310° angle FAQ
What type of angle is 310°?
A 310° angle is a reflex angle, because it is between 180° and 360°.
Does a 310° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 310° is already larger than both. What it does have is an explement (conjugate) of 50°, the angle that completes a full 360° circle.
How many radians is 310 degrees?
310° = 31π/18 radians ≈ 5.4105 rad. To convert degrees to radians, multiply by π/180: 310 × π/180 = 31π/18.
How do I measure a 310° angle on my screen?
Open the online protractor with 310° preset, or type 310 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
