At 100°, this is an obtuse angle, opened up past a square corner but not yet flat. Its supplement is 80°, so a 100° angle and an 80° angle side by side make a straight line.
100° is 5/18 of a full circle, or 5π/9 radians. If you face north and turn 100° clockwise, you end up facing between E and ESE (closest to east (E)).
100° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 80° |
| Explement (adds to 360°) | 260° |
| Radians | 5π/9 ≈ 1.745329 |
| Gradians | 111.1111 grad |
| Fraction of a turn | 5/18 (27.78%) |
| Degrees, minutes, seconds | 100° 0′ 0″ |
| Compass bearing | between E and ESE (closest to east (E)) |
Trigonometric values of 100°
| Function | Value |
|---|---|
| sin 100° | 0.984808 |
| cos 100° | −0.173648 |
| tan 100° | −5.671282 |
100° on a protractor
How to draw a 100° 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 100° 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 100°.
Drawing it a 100° angle without a protractor (rise and run method)
- 100° = 180° − 80°. Draw a straight line, pick a vertex on it, and build an 80° angle on one side as follows; the angle on the other side of the new line is 100°.
- Draw a straight baseline and measure 1.76 inches (about 1 3/4″) 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 80°, because tan 80° ≈ 5.6713.
Where you see 100° angles
- Aircraft fasteners and some sheet-metal screws use a 100° countersink.
- The Earth turns 100° on its axis in about 6 h 40 min.
- Obtuse angles like 100° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
100° angle FAQ
What type of angle is 100°?
A 100° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 100°?
The supplement of 100° is 80°, because 100° + 80° = 180°. A 100° angle has no complement, because it is already larger than 90°.
How many radians is 100 degrees?
100° = 5π/9 radians ≈ 1.7453 rad. To convert degrees to radians, multiply by π/180: 100 × π/180 = 5π/9.
How do I measure a 100° angle on my screen?
Open the online protractor with 100° preset, or type 100 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
