At 340°, this is a reflex angle, which goes more than halfway around a circle. It is the "outside" of a 20° angle: together they make a full 360° circle.
340° is 17/18 of a full circle, or 17π/9 radians. If you face north and turn 340° clockwise, you end up facing between NNW and N (closest to north-northwest (NNW)).
340° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 20° |
| Radians | 17π/9 ≈ 5.934119 |
| Gradians | 377.7778 grad |
| Fraction of a turn | 17/18 (94.44%) |
| Degrees, minutes, seconds | 340° 0′ 0″ |
| Compass bearing | between NNW and N (closest to north-northwest (NNW)) |
Trigonometric values of 340°
| Function | Value |
|---|---|
| sin 340° | −0.34202 |
| cos 340° | 0.939693 |
| tan 340° | −0.36397 |
340° on a protractor
How to draw a 340° angle with a protractor
- Subtract from 360°: 360° − 340° = 20°. 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 20°.
- Join the vertex to the dot. The inside angle is 20°; the outside angle, going the long way around, is 340°. Draw the angle arc on the outside and label it 340°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 340° directly.
Drawing it a 340° 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 3.64 inches (about 3 5/8″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 20°, because tan 20° ≈ 0.364.
- That gives you 20°. The outside (reflex) angle is 340°.
Where you see 340° angles
- The Earth turns 340° on its axis in about 22 h 40 min.
- A 340° 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
340° angle FAQ
What type of angle is 340°?
A 340° angle is a reflex angle, because it is between 180° and 360°.
Does a 340° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 340° is already larger than both. What it does have is an explement (conjugate) of 20°, the angle that completes a full 360° circle.
How many radians is 340 degrees?
340° = 17π/9 radians ≈ 5.9341 rad. To convert degrees to radians, multiply by π/180: 340 × π/180 = 17π/9.
How do I measure a 340° angle on my screen?
Open the online protractor with 340° preset, or type 340 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
