A 207° 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 153° angle: together they make a full 360° circle.
207° is 23/40 of a full circle, or 23π/20 radians. If you face north and turn 207° clockwise, you end up facing between SSW and SW (closest to south-southwest (SSW)).
207° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 153° |
| Radians | 23π/20 ≈ 3.612832 |
| Gradians | 230 grad |
| Fraction of a turn | 23/40 (57.5%) |
| Degrees, minutes, seconds | 207° 0′ 0″ |
| Compass bearing | between SSW and SW (closest to south-southwest (SSW)) |
Trigonometric values of 207°
| Function | Value |
|---|---|
| sin 207° | −0.45399 |
| cos 207° | −0.891007 |
| tan 207° | 0.509525 |
207° on a protractor
How to draw a 207° angle with a protractor
- Subtract from 360°: 360° − 207° = 153°. 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 153°.
- Join the vertex to the dot. The inside angle is 153°; the outside angle, going the long way around, is 207°. Draw the angle arc on the outside and label it 207°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 207° directly.
Drawing it a 207° angle without a protractor (rise and run method)
- 207° = 180° − 27°. Draw a straight line, pick a vertex on it, and build a 27° angle on one side as follows; the angle on the other side of the new line is 153°.
- 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 5.1 inches (about 5 1/8″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 27°, because tan 27° ≈ 0.5095.
- That gives you 153°. The outside (reflex) angle is 207°.
Where you see 207° angles
- The Earth turns 207° on its axis in about 13 h 48 min.
- A 207° 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
207° angle FAQ
What type of angle is 207°?
A 207° angle is a reflex angle, because it is between 180° and 360°.
Does a 207° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 207° is already larger than both. What it does have is an explement (conjugate) of 153°, the angle that completes a full 360° circle.
How many radians is 207 degrees?
207° = 23π/20 radians ≈ 3.6128 rad. To convert degrees to radians, multiply by π/180: 207 × π/180 = 23π/20.
How do I measure a 207° angle on my screen?
Open the online protractor with 207° preset, or type 207 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
