A 123° angle is an obtuse angle: wider than a right angle (90°) but less than a straight line (180°). Its supplement is 57°, so a 123° angle and a 57° angle side by side make a straight line.
123° is 41/120 of a full circle, or 41π/60 radians. If you face north and turn 123° clockwise, you end up facing between ESE and SE (closest to east-southeast (ESE)).
123° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 57° |
| Explement (adds to 360°) | 237° |
| Radians | 41π/60 ≈ 2.146755 |
| Gradians | 136.6667 grad |
| Fraction of a turn | 41/120 (34.17%) |
| Degrees, minutes, seconds | 123° 0′ 0″ |
| Compass bearing | between ESE and SE (closest to east-southeast (ESE)) |
Trigonometric values of 123°
| Function | Value |
|---|---|
| sin 123° | 0.838671 |
| cos 123° | −0.544639 |
| tan 123° | −1.539865 |
123° on a protractor
How to draw a 123° 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 123° 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 123°.
Drawing it a 123° angle without a protractor (rise and run method)
- 123° = 180° − 57°. Draw a straight line, pick a vertex on it, and build a 57° angle on one side as follows; the angle on the other side of the new line is 123°.
- Draw a straight baseline and measure 6.49 inches (about 6 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 57°, because tan 57° ≈ 1.5399.
Where you see 123° angles
- The Earth turns 123° on its axis in about 8 h 12 min.
- Obtuse angles like 123° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
123° angle FAQ
What type of angle is 123°?
A 123° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 123°?
The supplement of 123° is 57°, because 123° + 57° = 180°. A 123° angle has no complement, because it is already larger than 90°.
How many radians is 123 degrees?
123° = 41π/60 radians ≈ 2.1468 rad. To convert degrees to radians, multiply by π/180: 123 × π/180 = 41π/60.
How do I measure a 123° angle on my screen?
Open the online protractor with 123° preset, or type 123 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
