A 204° 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 156° angle: together they make a full 360° circle.
204° is 17/30 of a full circle, or 17π/15 radians. The minute hand of a clock sweeps 204° in 34 minutes. If you face north and turn 204° clockwise, you end up facing between SSW and SW (closest to south-southwest (SSW)).
204° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 156° |
| Radians | 17π/15 ≈ 3.560472 |
| Gradians | 226.6667 grad |
| Fraction of a turn | 17/30 (56.67%) |
| Degrees, minutes, seconds | 204° 0′ 0″ |
| Compass bearing | between SSW and SW (closest to south-southwest (SSW)) |
Trigonometric values of 204°
| Function | Value |
|---|---|
| sin 204° | −0.406737 |
| cos 204° | −0.913545 |
| tan 204° | 0.445229 |
204° on a protractor
How to draw a 204° angle with a protractor
- Subtract from 360°: 360° − 204° = 156°. 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 156°.
- Join the vertex to the dot. The inside angle is 156°; the outside angle, going the long way around, is 204°. Draw the angle arc on the outside and label it 204°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 204° directly.
Drawing it a 204° angle without a protractor (rise and run method)
- 204° = 180° − 24°. Draw a straight line, pick a vertex on it, and build a 24° angle on one side as follows; the angle on the other side of the new line is 156°.
- 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 4.45 inches (about 4 7/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 24°, because tan 24° ≈ 0.4452.
- That gives you 156°. The outside (reflex) angle is 204°.
Where you see 204° angles
- The Earth turns 204° on its axis in about 13 h 36 min.
- A 204° 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
204° angle FAQ
What type of angle is 204°?
A 204° angle is a reflex angle, because it is between 180° and 360°.
Does a 204° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 204° is already larger than both. What it does have is an explement (conjugate) of 156°, the angle that completes a full 360° circle.
How many radians is 204 degrees?
204° = 17π/15 radians ≈ 3.5605 rad. To convert degrees to radians, multiply by π/180: 204 × π/180 = 17π/15.
How do I measure a 204° angle on my screen?
Open the online protractor with 204° preset, or type 204 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
