A 320° angle is reflex because it measures between 180° and 360°. It is the "outside" of a 40° angle: together they make a full 360° circle.
320° is 8/9 of a full circle, or 16π/9 radians. If you face north and turn 320° clockwise, you end up facing between NW and NNW (closest to northwest (NW)).
320° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 40° |
| Radians | 16π/9 ≈ 5.585054 |
| Gradians | 355.5556 grad |
| Fraction of a turn | 8/9 (88.89%) |
| Degrees, minutes, seconds | 320° 0′ 0″ |
| Compass bearing | between NW and NNW (closest to northwest (NW)) |
Trigonometric values of 320°
| Function | Value |
|---|---|
| sin 320° | −0.642788 |
| cos 320° | 0.766044 |
| tan 320° | −0.8391 |
320° on a protractor
How to draw a 320° angle with a protractor
- Subtract from 360°: 360° − 320° = 40°. 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 40°.
- Join the vertex to the dot. The inside angle is 40°; the outside angle, going the long way around, is 320°. Draw the angle arc on the outside and label it 320°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 320° directly.
Drawing it a 320° angle without a protractor (rise and run method)
- Draw a straight baseline and measure exactly 10 inches along it from the vertex.
- At the 10-inch mark, draw a short line straight up at 90° (use a carpenter's square or the corner of a sheet of paper).
- Measure 8.39 inches (about 8 3/8″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 40°, because tan 40° ≈ 0.8391.
- That gives you 40°. The outside (reflex) angle is 320°.
Where you see 320° angles
- The Earth turns 320° on its axis in about 21 h 20 min.
- A 320° 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
320° angle FAQ
What type of angle is 320°?
A 320° angle is a reflex angle, because it is between 180° and 360°.
Does a 320° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 320° is already larger than both. What it does have is an explement (conjugate) of 40°, the angle that completes a full 360° circle.
How many radians is 320 degrees?
320° = 16π/9 radians ≈ 5.5851 rad. To convert degrees to radians, multiply by π/180: 320 × π/180 = 16π/9.
How do I measure a 320° angle on my screen?
Open the online protractor with 320° preset, or type 320 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
