At 217°, this is a reflex angle, which goes more than halfway around a circle. It is the "outside" of a 143° angle: together they make a full 360° circle.
217° is 217/360 of a full circle, or 217π/180 radians. If you face north and turn 217° clockwise, you end up facing between SSW and SW (closest to southwest (SW)).
217° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 143° |
| Radians | 217π/180 ≈ 3.787364 |
| Gradians | 241.1111 grad |
| Fraction of a turn | 217/360 (60.28%) |
| Degrees, minutes, seconds | 217° 0′ 0″ |
| Compass bearing | between SSW and SW (closest to southwest (SW)) |
Trigonometric values of 217°
| Function | Value |
|---|---|
| sin 217° | −0.601815 |
| cos 217° | −0.798636 |
| tan 217° | 0.753554 |
217° on a protractor
How to draw a 217° angle with a protractor
- Subtract from 360°: 360° − 217° = 143°. 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 143°.
- Join the vertex to the dot. The inside angle is 143°; the outside angle, going the long way around, is 217°. Draw the angle arc on the outside and label it 217°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 217° directly.
Drawing it a 217° angle without a protractor (rise and run method)
- 217° = 180° − 37°. Draw a straight line, pick a vertex on it, and build a 37° angle on one side as follows; the angle on the other side of the new line is 143°.
- 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 7.54 inches (about 7 9/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 37°, because tan 37° ≈ 0.7536.
- That gives you 143°. The outside (reflex) angle is 217°.
Where you see 217° angles
- The Earth turns 217° on its axis in about 14 h 28 min.
- A 217° 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
217° angle FAQ
What type of angle is 217°?
A 217° angle is a reflex angle, because it is between 180° and 360°.
Does a 217° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 217° is already larger than both. What it does have is an explement (conjugate) of 143°, the angle that completes a full 360° circle.
How many radians is 217 degrees?
217° = 217π/180 radians ≈ 3.7874 rad. To convert degrees to radians, multiply by π/180: 217 × π/180 = 217π/180.
How do I measure a 217° angle on my screen?
Open the online protractor with 217° preset, or type 217 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
