At 259°, this is a reflex angle, which goes more than halfway around a circle. It is the "outside" of a 101° angle: together they make a full 360° circle.
259° is 259/360 of a full circle, or 259π/180 radians. If you face north and turn 259° clockwise, you end up facing between WSW and W (closest to west (W)).
259° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 101° |
| Radians | 259π/180 ≈ 4.520403 |
| Gradians | 287.7778 grad |
| Fraction of a turn | 259/360 (71.94%) |
| Degrees, minutes, seconds | 259° 0′ 0″ |
| Compass bearing | between WSW and W (closest to west (W)) |
Trigonometric values of 259°
| Function | Value |
|---|---|
| sin 259° | −0.981627 |
| cos 259° | −0.190809 |
| tan 259° | 5.144554 |
259° on a protractor
How to draw a 259° angle with a protractor
- Subtract from 360°: 360° − 259° = 101°. 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 101°.
- Join the vertex to the dot. The inside angle is 101°; the outside angle, going the long way around, is 259°. Draw the angle arc on the outside and label it 259°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 259° directly.
Drawing it a 259° angle without a protractor (rise and run method)
- 259° = 180° − 79°. Draw a straight line, pick a vertex on it, and build a 79° angle on one side as follows; the angle on the other side of the new line is 101°.
- Draw a straight baseline and measure 1.94 inches (about 1 15/16″) 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 79°, because tan 79° ≈ 5.1446.
- That gives you 101°. The outside (reflex) angle is 259°.
Where you see 259° angles
- The Earth turns 259° on its axis in about 17 h 16 min.
- A 259° 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
259° angle FAQ
What type of angle is 259°?
A 259° angle is a reflex angle, because it is between 180° and 360°.
Does a 259° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 259° is already larger than both. What it does have is an explement (conjugate) of 101°, the angle that completes a full 360° circle.
How many radians is 259 degrees?
259° = 259π/180 radians ≈ 4.5204 rad. To convert degrees to radians, multiply by π/180: 259 × π/180 = 259π/180.
How do I measure a 259° angle on my screen?
Open the online protractor with 259° preset, or type 259 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
