A 299° angle is reflex because it measures between 180° and 360°. It is the "outside" of a 61° angle: together they make a full 360° circle.
299° is 299/360 of a full circle, or 299π/180 radians. If you face north and turn 299° clockwise, you end up facing between WNW and NW (closest to west-northwest (WNW)).
299° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 61° |
| Radians | 299π/180 ≈ 5.218534 |
| Gradians | 332.2222 grad |
| Fraction of a turn | 299/360 (83.06%) |
| Degrees, minutes, seconds | 299° 0′ 0″ |
| Compass bearing | between WNW and NW (closest to west-northwest (WNW)) |
Trigonometric values of 299°
| Function | Value |
|---|---|
| sin 299° | −0.87462 |
| cos 299° | 0.48481 |
| tan 299° | −1.804048 |
299° on a protractor
How to draw a 299° angle with a protractor
- Subtract from 360°: 360° − 299° = 61°. 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 61°.
- Join the vertex to the dot. The inside angle is 61°; the outside angle, going the long way around, is 299°. Draw the angle arc on the outside and label it 299°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 299° directly.
Drawing it a 299° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 5.54 inches (about 5 9/16″) 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 61°, because tan 61° ≈ 1.804.
- That gives you 61°. The outside (reflex) angle is 299°.
Where you see 299° angles
- The Earth turns 299° on its axis in about 19 h 56 min.
- A 299° 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
299° angle FAQ
What type of angle is 299°?
A 299° angle is a reflex angle, because it is between 180° and 360°.
Does a 299° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 299° is already larger than both. What it does have is an explement (conjugate) of 61°, the angle that completes a full 360° circle.
How many radians is 299 degrees?
299° = 299π/180 radians ≈ 5.2185 rad. To convert degrees to radians, multiply by π/180: 299 × π/180 = 299π/180.
How do I measure a 299° angle on my screen?
Open the online protractor with 299° preset, or type 299 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
