A 213° 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 147° angle: together they make a full 360° circle.
213° is 71/120 of a full circle, or 71π/60 radians. If you face north and turn 213° clockwise, you end up facing between SSW and SW (closest to south-southwest (SSW)).
213° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 147° |
| Radians | 71π/60 ≈ 3.717551 |
| Gradians | 236.6667 grad |
| Fraction of a turn | 71/120 (59.17%) |
| Degrees, minutes, seconds | 213° 0′ 0″ |
| Compass bearing | between SSW and SW (closest to south-southwest (SSW)) |
Trigonometric values of 213°
| Function | Value |
|---|---|
| sin 213° | −0.544639 |
| cos 213° | −0.838671 |
| tan 213° | 0.649408 |
213° on a protractor
How to draw a 213° angle with a protractor
- Subtract from 360°: 360° − 213° = 147°. 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 147°.
- Join the vertex to the dot. The inside angle is 147°; the outside angle, going the long way around, is 213°. Draw the angle arc on the outside and label it 213°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 213° directly.
Drawing it a 213° angle without a protractor (rise and run method)
- 213° = 180° − 33°. Draw a straight line, pick a vertex on it, and build a 33° angle on one side as follows; the angle on the other side of the new line is 147°.
- 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 6.49 inches (about 6 1/2″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 33°, because tan 33° ≈ 0.6494.
- That gives you 147°. The outside (reflex) angle is 213°.
Where you see 213° angles
- The Earth turns 213° on its axis in about 14 h 12 min.
- A 213° 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
213° angle FAQ
What type of angle is 213°?
A 213° angle is a reflex angle, because it is between 180° and 360°.
Does a 213° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 213° is already larger than both. What it does have is an explement (conjugate) of 147°, the angle that completes a full 360° circle.
How many radians is 213 degrees?
213° = 71π/60 radians ≈ 3.7176 rad. To convert degrees to radians, multiply by π/180: 213 × π/180 = 71π/60.
How do I measure a 213° angle on my screen?
Open the online protractor with 213° preset, or type 213 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
