At 118°, this is an obtuse angle, opened up past a square corner but not yet flat. Its supplement is 62°, so a 118° angle and a 62° angle side by side make a straight line.
118° is 59/180 of a full circle, or 59π/90 radians. If you face north and turn 118° clockwise, you end up facing between ESE and SE (closest to east-southeast (ESE)).
118° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 62° |
| Explement (adds to 360°) | 242° |
| Radians | 59π/90 ≈ 2.059489 |
| Gradians | 131.1111 grad |
| Fraction of a turn | 59/180 (32.78%) |
| Degrees, minutes, seconds | 118° 0′ 0″ |
| Compass bearing | between ESE and SE (closest to east-southeast (ESE)) |
Trigonometric values of 118°
| Function | Value |
|---|---|
| sin 118° | 0.882948 |
| cos 118° | −0.469472 |
| tan 118° | −1.880726 |
118° on a protractor
How to draw a 118° 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 118° 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 118°.
Drawing it a 118° angle without a protractor (rise and run method)
- 118° = 180° − 62°. Draw a straight line, pick a vertex on it, and build a 62° angle on one side as follows; the angle on the other side of the new line is 118°.
- Draw a straight baseline and measure 5.32 inches (about 5 5/16″) 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 62°, because tan 62° ≈ 1.8807.
Where you see 118° angles
- Standard general-purpose twist drill bits have a 118° point angle.
- The Earth turns 118° on its axis in about 7 h 52 min.
- Obtuse angles like 118° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
118° angle FAQ
What type of angle is 118°?
A 118° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 118°?
The supplement of 118° is 62°, because 118° + 62° = 180°. A 118° angle has no complement, because it is already larger than 90°.
How many radians is 118 degrees?
118° = 59π/90 radians ≈ 2.0595 rad. To convert degrees to radians, multiply by π/180: 118 × π/180 = 59π/90.
How do I measure a 118° angle on my screen?
Open the online protractor with 118° preset, or type 118 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
