A 351° angle is a reflex angle: it is bigger than a straight line (180°) but less than a full turn (360°). It is the "outside" of a 9° angle: together they make a full 360° circle.
351° is 39/40 of a full circle, or 39π/20 radians. If you face north and turn 351° clockwise, you end up facing between NNW and N (closest to north (N)).
351° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 9° |
| Radians | 39π/20 ≈ 6.126106 |
| Gradians | 390 grad |
| Fraction of a turn | 39/40 (97.5%) |
| Degrees, minutes, seconds | 351° 0′ 0″ |
| Compass bearing | between NNW and N (closest to north (N)) |
Trigonometric values of 351°
| Function | Value |
|---|---|
| sin 351° | −0.156434 |
| cos 351° | 0.987688 |
| tan 351° | −0.158384 |
351° on a protractor
How to draw a 351° angle with a protractor
- Subtract from 360°: 360° − 351° = 9°. 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 9°.
- Join the vertex to the dot. The inside angle is 9°; the outside angle, going the long way around, is 351°. Draw the angle arc on the outside and label it 351°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 351° directly.
Drawing it a 351° 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 1.58 inches (about 1 9/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 9°, because tan 9° ≈ 0.1584.
- That gives you 9°. The outside (reflex) angle is 351°.
Where you see 351° angles
- The Earth turns 351° on its axis in about 23 h 24 min.
- A 351° 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
351° angle FAQ
What type of angle is 351°?
A 351° angle is a reflex angle, because it is between 180° and 360°.
Does a 351° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 351° is already larger than both. What it does have is an explement (conjugate) of 9°, the angle that completes a full 360° circle.
How many radians is 351 degrees?
351° = 39π/20 radians ≈ 6.1261 rad. To convert degrees to radians, multiply by π/180: 351 × π/180 = 39π/20.
How do I measure a 351° angle on my screen?
Open the online protractor with 351° preset, or type 351 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
