At 355°, this is a reflex angle, which goes more than halfway around a circle. It is the "outside" of a 5° angle: together they make a full 360° circle.
355° is 71/72 of a full circle, or 71π/36 radians. If you face north and turn 355° clockwise, you end up facing between NNW and N (closest to north (N)).
355° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 5° |
| Radians | 71π/36 ≈ 6.195919 |
| Gradians | 394.4444 grad |
| Fraction of a turn | 71/72 (98.61%) |
| Degrees, minutes, seconds | 355° 0′ 0″ |
| Compass bearing | between NNW and N (closest to north (N)) |
Trigonometric values of 355°
| Function | Value |
|---|---|
| sin 355° | −0.087156 |
| cos 355° | 0.996195 |
| tan 355° | −0.087489 |
355° on a protractor
How to draw a 355° angle with a protractor
- Subtract from 360°: 360° − 355° = 5°. 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 5°.
- Join the vertex to the dot. The inside angle is 5°; the outside angle, going the long way around, is 355°. Draw the angle arc on the outside and label it 355°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 355° directly.
Drawing it a 355° 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 0.87 inches (about 7/8″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 5°, because tan 5° ≈ 0.0875.
- That gives you 5°. The outside (reflex) angle is 355°.
Where you see 355° angles
- The Earth turns 355° on its axis in about 23 h 40 min.
- A 355° 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
355° angle FAQ
What type of angle is 355°?
A 355° angle is a reflex angle, because it is between 180° and 360°.
Does a 355° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 355° is already larger than both. What it does have is an explement (conjugate) of 5°, the angle that completes a full 360° circle.
How many radians is 355 degrees?
355° = 71π/36 radians ≈ 6.1959 rad. To convert degrees to radians, multiply by π/180: 355 × π/180 = 71π/36.
How do I measure a 355° angle on my screen?
Open the online protractor with 355° preset, or type 355 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
