A 357° 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 3° angle: together they make a full 360° circle.
357° is 119/120 of a full circle, or 119π/60 radians. If you face north and turn 357° clockwise, you end up facing between NNW and N (closest to north (N)).
357° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 3° |
| Radians | 119π/60 ≈ 6.230825 |
| Gradians | 396.6667 grad |
| Fraction of a turn | 119/120 (99.17%) |
| Degrees, minutes, seconds | 357° 0′ 0″ |
| Compass bearing | between NNW and N (closest to north (N)) |
Trigonometric values of 357°
| Function | Value |
|---|---|
| sin 357° | −0.052336 |
| cos 357° | 0.99863 |
| tan 357° | −0.052408 |
357° on a protractor
How to draw a 357° angle with a protractor
- Subtract from 360°: 360° − 357° = 3°. 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 3°.
- Join the vertex to the dot. The inside angle is 3°; the outside angle, going the long way around, is 357°. Draw the angle arc on the outside and label it 357°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 357° directly.
Drawing it a 357° 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 0.52 inches (about 1/2″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 3°, because tan 3° ≈ 0.0524.
- That gives you 3°. The outside (reflex) angle is 357°.
Where you see 357° angles
- The Earth turns 357° on its axis in about 23 h 48 min.
- A 357° 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
357° angle FAQ
What type of angle is 357°?
A 357° angle is a reflex angle, because it is between 180° and 360°.
Does a 357° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 357° is already larger than both. What it does have is an explement (conjugate) of 3°, the angle that completes a full 360° circle.
How many radians is 357 degrees?
357° = 119π/60 radians ≈ 6.2308 rad. To convert degrees to radians, multiply by π/180: 357 × π/180 = 119π/60.
How do I measure a 357° angle on my screen?
Open the online protractor with 357° preset, or type 357 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
