A 260° angle is reflex because it measures between 180° and 360°. It is the "outside" of a 100° angle: together they make a full 360° circle.
260° is 13/18 of a full circle, or 13π/9 radians. If you face north and turn 260° clockwise, you end up facing between WSW and W (closest to west (W)).
260° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 100° |
| Radians | 13π/9 ≈ 4.537856 |
| Gradians | 288.8889 grad |
| Fraction of a turn | 13/18 (72.22%) |
| Degrees, minutes, seconds | 260° 0′ 0″ |
| Compass bearing | between WSW and W (closest to west (W)) |
Trigonometric values of 260°
| Function | Value |
|---|---|
| sin 260° | −0.984808 |
| cos 260° | −0.173648 |
| tan 260° | 5.671282 |
260° on a protractor
How to draw a 260° angle with a protractor
- Subtract from 360°: 360° − 260° = 100°. 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 100°.
- Join the vertex to the dot. The inside angle is 100°; the outside angle, going the long way around, is 260°. Draw the angle arc on the outside and label it 260°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 260° directly.
Drawing it a 260° angle without a protractor (rise and run method)
- 260° = 180° − 80°. Draw a straight line, pick a vertex on it, and build an 80° angle on one side as follows; the angle on the other side of the new line is 100°.
- Draw a straight baseline and measure 1.76 inches (about 1 3/4″) 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 80°, because tan 80° ≈ 5.6713.
- That gives you 100°. The outside (reflex) angle is 260°.
Where you see 260° angles
- The Earth turns 260° on its axis in about 17 h 20 min.
- A 260° 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
260° angle FAQ
What type of angle is 260°?
A 260° angle is a reflex angle, because it is between 180° and 360°.
Does a 260° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 260° is already larger than both. What it does have is an explement (conjugate) of 100°, the angle that completes a full 360° circle.
How many radians is 260 degrees?
260° = 13π/9 radians ≈ 4.5379 rad. To convert degrees to radians, multiply by π/180: 260 × π/180 = 13π/9.
How do I measure a 260° angle on my screen?
Open the online protractor with 260° preset, or type 260 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
