A 210° 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 150° angle: together they make a full 360° circle.
210° is 7/12 of a full circle, or 7π/6 radians. The minute hand of a clock sweeps 210° in 35 minutes. If you face north and turn 210° clockwise, you end up facing between SSW and SW (closest to south-southwest (SSW)).
210° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 150° |
| Radians | 7π/6 ≈ 3.665191 |
| Gradians | 233.3333 grad |
| Fraction of a turn | 7/12 (58.33%) |
| Degrees, minutes, seconds | 210° 0′ 0″ |
| Compass bearing | between SSW and SW (closest to south-southwest (SSW)) |
Trigonometric values of 210°
| Function | Value |
|---|---|
| sin 210° | −1/2 ≈ −0.5 |
| cos 210° | −√3/2 ≈ −0.866025 |
| tan 210° | √3/3 ≈ 0.57735 |
210° on a protractor
How to draw a 210° angle with a protractor
- Subtract from 360°: 360° − 210° = 150°. 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 150°.
- Join the vertex to the dot. The inside angle is 150°; the outside angle, going the long way around, is 210°. Draw the angle arc on the outside and label it 210°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 210° directly.
Drawing it a 210° angle without a protractor (compass and ruler)
- Draw a 180° angle: draw a straight line.
- Inside it, starting from the second arm, mark a 30° angle: construct a 60° angle, then bisect it.
- What is left between the first arm and the new line is 180° − 30° = 150°.
- That gives you 150°. The reflex angle on the outside of it is 210°.
Where you see 210° angles
- The Earth turns 210° on its axis in about 14 hours.
- A 210° 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
210° angle FAQ
What type of angle is 210°?
A 210° angle is a reflex angle, because it is between 180° and 360°.
Does a 210° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 210° is already larger than both. What it does have is an explement (conjugate) of 150°, the angle that completes a full 360° circle.
How many radians is 210 degrees?
210° = 7π/6 radians ≈ 3.6652 rad. To convert degrees to radians, multiply by π/180: 210 × π/180 = 7π/6.
How do I measure a 210° angle on my screen?
Open the online protractor with 210° preset, or type 210 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
