At 205°, this is a reflex angle, which goes more than halfway around a circle. It is the "outside" of a 155° angle: together they make a full 360° circle.
205° is 41/72 of a full circle, or 41π/36 radians. If you face north and turn 205° clockwise, you end up facing between SSW and SW (closest to south-southwest (SSW)).
205° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 155° |
| Radians | 41π/36 ≈ 3.577925 |
| Gradians | 227.7778 grad |
| Fraction of a turn | 41/72 (56.94%) |
| Degrees, minutes, seconds | 205° 0′ 0″ |
| Compass bearing | between SSW and SW (closest to south-southwest (SSW)) |
Trigonometric values of 205°
| Function | Value |
|---|---|
| sin 205° | −0.422618 |
| cos 205° | −0.906308 |
| tan 205° | 0.466308 |
205° on a protractor
How to draw a 205° angle with a protractor
- Subtract from 360°: 360° − 205° = 155°. 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 155°.
- Join the vertex to the dot. The inside angle is 155°; the outside angle, going the long way around, is 205°. Draw the angle arc on the outside and label it 205°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 205° directly.
Drawing it a 205° angle without a protractor (rise and run method)
- 205° = 180° − 25°. Draw a straight line, pick a vertex on it, and build a 25° angle on one side as follows; the angle on the other side of the new line is 155°.
- 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 4.66 inches (about 4 11/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 25°, because tan 25° ≈ 0.4663.
- That gives you 155°. The outside (reflex) angle is 205°.
Where you see 205° angles
- The Earth turns 205° on its axis in about 13 h 40 min.
- A 205° 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
205° angle FAQ
What type of angle is 205°?
A 205° angle is a reflex angle, because it is between 180° and 360°.
Does a 205° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 205° is already larger than both. What it does have is an explement (conjugate) of 155°, the angle that completes a full 360° circle.
How many radians is 205 degrees?
205° = 41π/36 radians ≈ 3.5779 rad. To convert degrees to radians, multiply by π/180: 205 × π/180 = 41π/36.
How do I measure a 205° angle on my screen?
Open the online protractor with 205° preset, or type 205 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
