A 222° 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 138° angle: together they make a full 360° circle.
222° is 37/60 of a full circle, or 37π/30 radians. The minute hand of a clock sweeps 222° in 37 minutes. If you face north and turn 222° clockwise, you end up facing between SSW and SW (closest to southwest (SW)).
222° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 138° |
| Radians | 37π/30 ≈ 3.874631 |
| Gradians | 246.6667 grad |
| Fraction of a turn | 37/60 (61.67%) |
| Degrees, minutes, seconds | 222° 0′ 0″ |
| Compass bearing | between SSW and SW (closest to southwest (SW)) |
Trigonometric values of 222°
| Function | Value |
|---|---|
| sin 222° | −0.669131 |
| cos 222° | −0.743145 |
| tan 222° | 0.900404 |
222° on a protractor
How to draw a 222° angle with a protractor
- Subtract from 360°: 360° − 222° = 138°. 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 138°.
- Join the vertex to the dot. The inside angle is 138°; the outside angle, going the long way around, is 222°. Draw the angle arc on the outside and label it 222°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 222° directly.
Drawing it a 222° angle without a protractor (rise and run method)
- 222° = 180° − 42°. Draw a straight line, pick a vertex on it, and build a 42° angle on one side as follows; the angle on the other side of the new line is 138°.
- 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 inches (about 9″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 42°, because tan 42° ≈ 0.9004.
- That gives you 138°. The outside (reflex) angle is 222°.
Where you see 222° angles
- The Earth turns 222° on its axis in about 14 h 48 min.
- A 222° 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
222° angle FAQ
What type of angle is 222°?
A 222° angle is a reflex angle, because it is between 180° and 360°.
Does a 222° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 222° is already larger than both. What it does have is an explement (conjugate) of 138°, the angle that completes a full 360° circle.
How many radians is 222 degrees?
222° = 37π/30 radians ≈ 3.8746 rad. To convert degrees to radians, multiply by π/180: 222 × π/180 = 37π/30.
How do I measure a 222° angle on my screen?
Open the online protractor with 222° preset, or type 222 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
