A 111° angle is an obtuse angle: wider than a right angle (90°) but less than a straight line (180°). Its supplement is 69°, so a 111° angle and a 69° angle side by side make a straight line.
111° is 37/120 of a full circle, or 37π/60 radians. If you face north and turn 111° clockwise, you end up facing between E and ESE (closest to east-southeast (ESE)).
111° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 69° |
| Explement (adds to 360°) | 249° |
| Radians | 37π/60 ≈ 1.937315 |
| Gradians | 123.3333 grad |
| Fraction of a turn | 37/120 (30.83%) |
| Degrees, minutes, seconds | 111° 0′ 0″ |
| Compass bearing | between E and ESE (closest to east-southeast (ESE)) |
Trigonometric values of 111°
| Function | Value |
|---|---|
| sin 111° | 0.93358 |
| cos 111° | −0.358368 |
| tan 111° | −2.605089 |
111° on a protractor
How to draw a 111° 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 111° 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 111°.
Drawing it a 111° angle without a protractor (rise and run method)
- 111° = 180° − 69°. Draw a straight line, pick a vertex on it, and build a 69° angle on one side as follows; the angle on the other side of the new line is 111°.
- Draw a straight baseline and measure 3.84 inches (about 3 13/16″) 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 69°, because tan 69° ≈ 2.6051.
Where you see 111° angles
- The Earth turns 111° on its axis in about 7 h 24 min.
- Obtuse angles like 111° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
111° angle FAQ
What type of angle is 111°?
A 111° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 111°?
The supplement of 111° is 69°, because 111° + 69° = 180°. A 111° angle has no complement, because it is already larger than 90°.
How many radians is 111 degrees?
111° = 37π/60 radians ≈ 1.9373 rad. To convert degrees to radians, multiply by π/180: 111 × π/180 = 37π/60.
How do I measure a 111° angle on my screen?
Open the online protractor with 111° preset, or type 111 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
