At 208°, this is a reflex angle, which goes more than halfway around a circle. It is the "outside" of a 152° angle: together they make a full 360° circle.
208° is 26/45 of a full circle, or 52π/45 radians. If you face north and turn 208° clockwise, you end up facing between SSW and SW (closest to south-southwest (SSW)).
208° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 152° |
| Radians | 52π/45 ≈ 3.630285 |
| Gradians | 231.1111 grad |
| Fraction of a turn | 26/45 (57.78%) |
| Degrees, minutes, seconds | 208° 0′ 0″ |
| Compass bearing | between SSW and SW (closest to south-southwest (SSW)) |
Trigonometric values of 208°
| Function | Value |
|---|---|
| sin 208° | −0.469472 |
| cos 208° | −0.882948 |
| tan 208° | 0.531709 |
208° on a protractor
How to draw a 208° angle with a protractor
- Subtract from 360°: 360° − 208° = 152°. 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 152°.
- Join the vertex to the dot. The inside angle is 152°; the outside angle, going the long way around, is 208°. Draw the angle arc on the outside and label it 208°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 208° directly.
Drawing it a 208° angle without a protractor (rise and run method)
- 208° = 180° − 28°. Draw a straight line, pick a vertex on it, and build a 28° angle on one side as follows; the angle on the other side of the new line is 152°.
- 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 5.32 inches (about 5 5/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 28°, because tan 28° ≈ 0.5317.
- That gives you 152°. The outside (reflex) angle is 208°.
Where you see 208° angles
- The Earth turns 208° on its axis in about 13 h 52 min.
- A 208° 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
208° angle FAQ
What type of angle is 208°?
A 208° angle is a reflex angle, because it is between 180° and 360°.
Does a 208° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 208° is already larger than both. What it does have is an explement (conjugate) of 152°, the angle that completes a full 360° circle.
How many radians is 208 degrees?
208° = 52π/45 radians ≈ 3.6303 rad. To convert degrees to radians, multiply by π/180: 208 × π/180 = 52π/45.
How do I measure a 208° angle on my screen?
Open the online protractor with 208° preset, or type 208 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
