A 219° angle is a reflex angle: it is bigger than a straight line (180°) but less than a full turn (360°). It is the "outside" of a 141° angle: together they make a full 360° circle.
219° is 73/120 of a full circle, or 73π/60 radians. If you face north and turn 219° clockwise, you end up facing between SSW and SW (closest to southwest (SW)).
219° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 141° |
| Radians | 73π/60 ≈ 3.822271 |
| Gradians | 243.3333 grad |
| Fraction of a turn | 73/120 (60.83%) |
| Degrees, minutes, seconds | 219° 0′ 0″ |
| Compass bearing | between SSW and SW (closest to southwest (SW)) |
Trigonometric values of 219°
| Function | Value |
|---|---|
| sin 219° | −0.62932 |
| cos 219° | −0.777146 |
| tan 219° | 0.809784 |
219° on a protractor
How to draw a 219° angle with a protractor
- Subtract from 360°: 360° − 219° = 141°. 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 141°.
- Join the vertex to the dot. The inside angle is 141°; the outside angle, going the long way around, is 219°. Draw the angle arc on the outside and label it 219°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 219° directly.
Drawing it a 219° angle without a protractor (rise and run method)
- 219° = 180° − 39°. Draw a straight line, pick a vertex on it, and build a 39° angle on one side as follows; the angle on the other side of the new line is 141°.
- 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 8.1 inches (about 8 1/8″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 39°, because tan 39° ≈ 0.8098.
- That gives you 141°. The outside (reflex) angle is 219°.
Where you see 219° angles
- The Earth turns 219° on its axis in about 14 h 36 min.
- A 219° 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
219° angle FAQ
What type of angle is 219°?
A 219° angle is a reflex angle, because it is between 180° and 360°.
Does a 219° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 219° is already larger than both. What it does have is an explement (conjugate) of 141°, the angle that completes a full 360° circle.
How many radians is 219 degrees?
219° = 73π/60 radians ≈ 3.8223 rad. To convert degrees to radians, multiply by π/180: 219 × π/180 = 73π/60.
How do I measure a 219° angle on my screen?
Open the online protractor with 219° preset, or type 219 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
