A 308° angle is reflex because it measures between 180° and 360°. It is the "outside" of a 52° angle: together they make a full 360° circle.
308° is 77/90 of a full circle, or 77π/45 radians. If you face north and turn 308° clockwise, you end up facing between WNW and NW (closest to northwest (NW)).
308° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 52° |
| Radians | 77π/45 ≈ 5.375614 |
| Gradians | 342.2222 grad |
| Fraction of a turn | 77/90 (85.56%) |
| Degrees, minutes, seconds | 308° 0′ 0″ |
| Compass bearing | between WNW and NW (closest to northwest (NW)) |
Trigonometric values of 308°
| Function | Value |
|---|---|
| sin 308° | −0.788011 |
| cos 308° | 0.615661 |
| tan 308° | −1.279942 |
308° on a protractor
How to draw a 308° angle with a protractor
- Subtract from 360°: 360° − 308° = 52°. 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 52°.
- Join the vertex to the dot. The inside angle is 52°; the outside angle, going the long way around, is 308°. Draw the angle arc on the outside and label it 308°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 308° directly.
Drawing it a 308° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 7.81 inches (about 7 13/16″) along it from the vertex.
- At that mark, draw a line straight up at 90° and measure exactly 10 inches up it.
- Join the top mark to the vertex. The angle at the vertex is 52°, because tan 52° ≈ 1.2799.
- That gives you 52°. The outside (reflex) angle is 308°.
Where you see 308° angles
- The Earth turns 308° on its axis in about 20 h 32 min.
- A 308° 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
308° angle FAQ
What type of angle is 308°?
A 308° angle is a reflex angle, because it is between 180° and 360°.
Does a 308° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 308° is already larger than both. What it does have is an explement (conjugate) of 52°, the angle that completes a full 360° circle.
How many radians is 308 degrees?
308° = 77π/45 radians ≈ 5.3756 rad. To convert degrees to radians, multiply by π/180: 308 × π/180 = 77π/45.
How do I measure a 308° angle on my screen?
Open the online protractor with 308° preset, or type 308 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
