A 108° angle is an obtuse angle: wider than a right angle (90°) but less than a straight line (180°). Its supplement is 72°, so a 108° angle and a 72° angle side by side make a straight line.
108° is 3/10 of a full circle, or 3π/5 radians. The minute hand of a clock sweeps 108° in 18 minutes. If you face north and turn 108° clockwise, you end up facing between E and ESE (closest to east-southeast (ESE)).
108° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 72° |
| Explement (adds to 360°) | 252° |
| Radians | 3π/5 ≈ 1.884956 |
| Gradians | 120 grad |
| Fraction of a turn | 3/10 (30%) |
| Degrees, minutes, seconds | 108° 0′ 0″ |
| Compass bearing | between E and ESE (closest to east-southeast (ESE)) |
Trigonometric values of 108°
| Function | Value |
|---|---|
| sin 108° | √(10 + 2√5)/4 ≈ 0.951057 |
| cos 108° | −(√5 − 1)/4 ≈ −0.309017 |
| tan 108° | −3.077684 |
108° on a protractor
How to draw a 108° 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 108° 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 108°.
Drawing it a 108° angle without a protractor (rise and run method)
- 108° = 180° − 72°. Draw a straight line, pick a vertex on it, and build a 72° angle on one side as follows; the angle on the other side of the new line is 108°.
- Draw a straight baseline and measure 3.25 inches (about 3 1/4″) 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 72°, because tan 72° ≈ 3.0777.
Where you see 108° angles
- Each interior corner of a regular pentagon measures 108°.
- The Earth turns 108° on its axis in about 7 h 12 min.
- Obtuse angles like 108° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
108° angle FAQ
What type of angle is 108°?
A 108° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 108°?
The supplement of 108° is 72°, because 108° + 72° = 180°. A 108° angle has no complement, because it is already larger than 90°.
How many radians is 108 degrees?
108° = 3π/5 radians ≈ 1.885 rad. To convert degrees to radians, multiply by π/180: 108 × π/180 = 3π/5.
How do I measure a 108° angle on my screen?
Open the online protractor with 108° preset, or type 108 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
