A 116° angle is obtuse because it is greater than 90° and less than 180°. Its supplement is 64°, so a 116° angle and a 64° angle side by side make a straight line.
116° is 29/90 of a full circle, or 29π/45 radians. If you face north and turn 116° clockwise, you end up facing between ESE and SE (closest to east-southeast (ESE)).
116° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 64° |
| Explement (adds to 360°) | 244° |
| Radians | 29π/45 ≈ 2.024582 |
| Gradians | 128.8889 grad |
| Fraction of a turn | 29/90 (32.22%) |
| Degrees, minutes, seconds | 116° 0′ 0″ |
| Compass bearing | between ESE and SE (closest to east-southeast (ESE)) |
Trigonometric values of 116°
| Function | Value |
|---|---|
| sin 116° | 0.898794 |
| cos 116° | −0.438371 |
| tan 116° | −2.050304 |
116° on a protractor
How to draw a 116° 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 116° 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 116°.
Drawing it a 116° angle without a protractor (rise and run method)
- 116° = 180° − 64°. Draw a straight line, pick a vertex on it, and build a 64° angle on one side as follows; the angle on the other side of the new line is 116°.
- Draw a straight baseline and measure 4.88 inches (about 4 7/8″) 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 64°, because tan 64° ≈ 2.0503.
Where you see 116° angles
- The Earth turns 116° on its axis in about 7 h 44 min.
- Obtuse angles like 116° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
116° angle FAQ
What type of angle is 116°?
A 116° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 116°?
The supplement of 116° is 64°, because 116° + 64° = 180°. A 116° angle has no complement, because it is already larger than 90°.
How many radians is 116 degrees?
116° = 29π/45 radians ≈ 2.0246 rad. To convert degrees to radians, multiply by π/180: 116 × π/180 = 29π/45.
How do I measure a 116° angle on my screen?
Open the online protractor with 116° preset, or type 116 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
