A 104° angle is obtuse because it is greater than 90° and less than 180°. Its supplement is 76°, so a 104° angle and a 76° angle side by side make a straight line.
104° is 13/45 of a full circle, or 26π/45 radians. If you face north and turn 104° clockwise, you end up facing between E and ESE (closest to east-southeast (ESE)).
104° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 76° |
| Explement (adds to 360°) | 256° |
| Radians | 26π/45 ≈ 1.815142 |
| Gradians | 115.5556 grad |
| Fraction of a turn | 13/45 (28.89%) |
| Degrees, minutes, seconds | 104° 0′ 0″ |
| Compass bearing | between E and ESE (closest to east-southeast (ESE)) |
Trigonometric values of 104°
| Function | Value |
|---|---|
| sin 104° | 0.970296 |
| cos 104° | −0.241922 |
| tan 104° | −4.010781 |
104° on a protractor
How to draw a 104° 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 104° 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 104°.
Drawing it a 104° angle without a protractor (rise and run method)
- 104° = 180° − 76°. Draw a straight line, pick a vertex on it, and build a 76° angle on one side as follows; the angle on the other side of the new line is 104°.
- Draw a straight baseline and measure 2.49 inches (about 2 1/2″) 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 76°, because tan 76° ≈ 4.0108.
Where you see 104° angles
- The H–O–H bond angle of a water molecule is about 104.5°.
- The Earth turns 104° on its axis in about 6 h 56 min.
- Obtuse angles like 104° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
104° angle FAQ
What type of angle is 104°?
A 104° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 104°?
The supplement of 104° is 76°, because 104° + 76° = 180°. A 104° angle has no complement, because it is already larger than 90°.
How many radians is 104 degrees?
104° = 26π/45 radians ≈ 1.8151 rad. To convert degrees to radians, multiply by π/180: 104 × π/180 = 26π/45.
How do I measure a 104° angle on my screen?
Open the online protractor with 104° preset, or type 104 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
