At 349°, this is a reflex angle, which goes more than halfway around a circle. It is the "outside" of an 11° angle: together they make a full 360° circle.
349° is 349/360 of a full circle, or 349π/180 radians. If you face north and turn 349° clockwise, you end up facing between NNW and N (closest to north (N)).
349° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 11° |
| Radians | 349π/180 ≈ 6.091199 |
| Gradians | 387.7778 grad |
| Fraction of a turn | 349/360 (96.94%) |
| Degrees, minutes, seconds | 349° 0′ 0″ |
| Compass bearing | between NNW and N (closest to north (N)) |
Trigonometric values of 349°
| Function | Value |
|---|---|
| sin 349° | −0.190809 |
| cos 349° | 0.981627 |
| tan 349° | −0.19438 |
349° on a protractor
How to draw a 349° angle with a protractor
- Subtract from 360°: 360° − 349° = 11°. 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 11°.
- Join the vertex to the dot. The inside angle is 11°; the outside angle, going the long way around, is 349°. Draw the angle arc on the outside and label it 349°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 349° directly.
Drawing it a 349° 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 1.94 inches (about 1 15/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 11°, because tan 11° ≈ 0.1944.
- That gives you 11°. The outside (reflex) angle is 349°.
Where you see 349° angles
- The Earth turns 349° on its axis in about 23 h 16 min.
- A 349° 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
349° angle FAQ
What type of angle is 349°?
A 349° angle is a reflex angle, because it is between 180° and 360°.
Does a 349° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 349° is already larger than both. What it does have is an explement (conjugate) of 11°, the angle that completes a full 360° circle.
How many radians is 349 degrees?
349° = 349π/180 radians ≈ 6.0912 rad. To convert degrees to radians, multiply by π/180: 349 × π/180 = 349π/180.
How do I measure a 349° angle on my screen?
Open the online protractor with 349° preset, or type 349 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
