At 91°, this is an obtuse angle, opened up past a square corner but not yet flat. Its supplement is 89°, so a 91° angle and an 89° angle side by side make a straight line.
91° is 91/360 of a full circle, or 91π/180 radians. If you face north and turn 91° clockwise, you end up facing between E and ESE (closest to east (E)).
91° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 89° |
| Explement (adds to 360°) | 269° |
| Radians | 91π/180 ≈ 1.58825 |
| Gradians | 101.1111 grad |
| Fraction of a turn | 91/360 (25.28%) |
| Degrees, minutes, seconds | 91° 0′ 0″ |
| Compass bearing | between E and ESE (closest to east (E)) |
Trigonometric values of 91°
| Function | Value |
|---|---|
| sin 91° | 0.999848 |
| cos 91° | −0.017452 |
| tan 91° | −57.289962 |
91° on a protractor
How to draw a 91° 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 91° 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 91°.
Drawing it a 91° angle without a protractor (rise and run method)
- 91° = 180° − 89°. Draw a straight line, pick a vertex on it, and build an 89° angle on one side as follows; the angle on the other side of the new line is 91°.
- Draw a straight baseline and measure 0.17 inches (about 3/16″) along it from the vertex.
- At that mark, draw a line straight up at 90° and measure exactly 10 inches up it.
- Join the top mark to the vertex. The angle at the vertex is 89°, because tan 89° ≈ 57.29.
Where you see 91° angles
- The Earth turns 91° on its axis in about 6 h 4 min.
- Obtuse angles like 91° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
91° angle FAQ
What type of angle is 91°?
A 91° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 91°?
The supplement of 91° is 89°, because 91° + 89° = 180°. A 91° angle has no complement, because it is already larger than 90°.
How many radians is 91 degrees?
91° = 91π/180 radians ≈ 1.5882 rad. To convert degrees to radians, multiply by π/180: 91 × π/180 = 91π/180.
How do I measure a 91° angle on my screen?
Open the online protractor with 91° preset, or type 91 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
