A 171° angle is an obtuse angle: wider than a right angle (90°) but less than a straight line (180°). Its supplement is 9°, so a 171° angle and a 9° angle side by side make a straight line.
171° is 19/40 of a full circle, or 19π/20 radians. If you face north and turn 171° clockwise, you end up facing between SSE and S (closest to south (S)).
171° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 9° |
| Explement (adds to 360°) | 189° |
| Radians | 19π/20 ≈ 2.984513 |
| Gradians | 190 grad |
| Fraction of a turn | 19/40 (47.5%) |
| Degrees, minutes, seconds | 171° 0′ 0″ |
| Compass bearing | between SSE and S (closest to south (S)) |
Trigonometric values of 171°
| Function | Value |
|---|---|
| sin 171° | 0.156434 |
| cos 171° | −0.987688 |
| tan 171° | −0.158384 |
171° on a protractor
How to draw a 171° angle with a protractor
- Draw a straight line with a ruler. This is the first arm; mark the vertex at one end.
- Place the center mark of the protractor exactly on the vertex and line up the 0° baseline with your line.
- Find 171° on the row of numbers that reads 0° on your line (protractors have two rows running in opposite directions) and make a small dot at the edge.
- Remove the protractor and draw a line from the vertex through the dot. Mark the angle with an arc and label it 171°.
Drawing it a 171° angle without a protractor (rise and run method)
- 171° = 180° − 9°. Draw a straight line, pick a vertex on it, and build a 9° angle on one side as follows; the angle on the other side of the new line is 171°.
- 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 1.58 inches (about 1 9/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 9°, because tan 9° ≈ 0.1584.
Where you see 171° angles
- Each interior corner of a regular 40-sided polygon measures 171°.
- The Earth turns 171° on its axis in about 11 h 24 min.
- Obtuse angles like 171° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
171° angle FAQ
What type of angle is 171°?
A 171° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 171°?
The supplement of 171° is 9°, because 171° + 9° = 180°. A 171° angle has no complement, because it is already larger than 90°.
How many radians is 171 degrees?
171° = 19π/20 radians ≈ 2.9845 rad. To convert degrees to radians, multiply by π/180: 171 × π/180 = 19π/20.
How do I measure a 171° angle on my screen?
Open the online protractor with 171° preset, or type 171 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
