At 223°, this is a reflex angle, which goes more than halfway around a circle. It is the "outside" of a 137° angle: together they make a full 360° circle.
223° is 223/360 of a full circle, or 223π/180 radians. If you face north and turn 223° clockwise, you end up facing between SSW and SW (closest to southwest (SW)).
223° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 137° |
| Radians | 223π/180 ≈ 3.892084 |
| Gradians | 247.7778 grad |
| Fraction of a turn | 223/360 (61.94%) |
| Degrees, minutes, seconds | 223° 0′ 0″ |
| Compass bearing | between SSW and SW (closest to southwest (SW)) |
Trigonometric values of 223°
| Function | Value |
|---|---|
| sin 223° | −0.681998 |
| cos 223° | −0.731354 |
| tan 223° | 0.932515 |
223° on a protractor
How to draw a 223° angle with a protractor
- Subtract from 360°: 360° − 223° = 137°. 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 137°.
- Join the vertex to the dot. The inside angle is 137°; the outside angle, going the long way around, is 223°. Draw the angle arc on the outside and label it 223°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 223° directly.
Drawing it a 223° angle without a protractor (rise and run method)
- 223° = 180° − 43°. Draw a straight line, pick a vertex on it, and build a 43° angle on one side as follows; the angle on the other side of the new line is 137°.
- 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 9.33 inches (about 9 5/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 43°, because tan 43° ≈ 0.9325.
- That gives you 137°. The outside (reflex) angle is 223°.
Where you see 223° angles
- The Earth turns 223° on its axis in about 14 h 52 min.
- A 223° 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
223° angle FAQ
What type of angle is 223°?
A 223° angle is a reflex angle, because it is between 180° and 360°.
Does a 223° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 223° is already larger than both. What it does have is an explement (conjugate) of 137°, the angle that completes a full 360° circle.
How many radians is 223 degrees?
223° = 223π/180 radians ≈ 3.8921 rad. To convert degrees to radians, multiply by π/180: 223 × π/180 = 223π/180.
How do I measure a 223° angle on my screen?
Open the online protractor with 223° preset, or type 223 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
