A 120° angle is an obtuse angle: wider than a right angle (90°) but less than a straight line (180°). Its supplement is 60°, so a 120° angle and a 60° angle side by side make a straight line.
120° is one third (1/3) of a full circle, or 2π/3 radians. The minute hand of a clock sweeps 120° in 20 minutes. If you face north and turn 120° clockwise, you end up facing between ESE and SE (closest to east-southeast (ESE)).
120° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 60° |
| Explement (adds to 360°) | 240° |
| Radians | 2π/3 ≈ 2.094395 |
| Gradians | 133.3333 grad |
| Fraction of a turn | one third (1/3) (33.33%) |
| Degrees, minutes, seconds | 120° 0′ 0″ |
| Compass bearing | between ESE and SE (closest to east-southeast (ESE)) |
Trigonometric values of 120°
| Function | Value |
|---|---|
| sin 120° | √3/2 ≈ 0.866025 |
| cos 120° | −1/2 ≈ −0.5 |
| tan 120° | −√3 ≈ −1.732051 |
120° on a protractor
How to draw a 120° 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 120° 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 120°.
Drawing it a 120° angle without a protractor (compass and ruler)
- Draw a 180° angle: draw a straight line.
- Inside it, starting from the second arm, mark a 60° angle: construct an equilateral triangle: with the compass set to the length of the base line, draw arcs from both ends; the crossing point makes a 60° angle with the base.
- What is left between the first arm and the new line is 180° − 60° = 120°.
Where you see 120° angles
- Each corner of a regular hexagon, like a honeycomb cell or a hex nut, is 120°.
- The three blades of a wind turbine are spaced 120° apart.
- At 4:00 the hands of a clock form a 120° angle.
- The Earth turns 120° on its axis in about 8 hours.
Related angles
120° angle FAQ
What type of angle is 120°?
A 120° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 120°?
The supplement of 120° is 60°, because 120° + 60° = 180°. A 120° angle has no complement, because it is already larger than 90°.
How many radians is 120 degrees?
120° = 2π/3 radians ≈ 2.0944 rad. To convert degrees to radians, multiply by π/180: 120 × π/180 = 2π/3.
How do I measure a 120° angle on my screen?
Open the online protractor with 120° preset, or type 120 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.