At 124°, this is an obtuse angle, opened up past a square corner but not yet flat. Its supplement is 56°, so a 124° angle and a 56° angle side by side make a straight line.
124° is 31/90 of a full circle, or 31π/45 radians. If you face north and turn 124° clockwise, you end up facing between ESE and SE (closest to southeast (SE)).
124° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 56° |
| Explement (adds to 360°) | 236° |
| Radians | 31π/45 ≈ 2.164208 |
| Gradians | 137.7778 grad |
| Fraction of a turn | 31/90 (34.44%) |
| Degrees, minutes, seconds | 124° 0′ 0″ |
| Compass bearing | between ESE and SE (closest to southeast (SE)) |
Trigonometric values of 124°
| Function | Value |
|---|---|
| sin 124° | 0.829038 |
| cos 124° | −0.559193 |
| tan 124° | −1.482561 |
124° on a protractor
How to draw a 124° 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 124° 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 124°.
Drawing it a 124° angle without a protractor (rise and run method)
- 124° = 180° − 56°. Draw a straight line, pick a vertex on it, and build a 56° angle on one side as follows; the angle on the other side of the new line is 124°.
- Draw a straight baseline and measure 6.75 inches (about 6 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 56°, because tan 56° ≈ 1.4826.
Where you see 124° angles
- The Earth turns 124° on its axis in about 8 h 16 min.
- Obtuse angles like 124° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
124° angle FAQ
What type of angle is 124°?
A 124° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 124°?
The supplement of 124° is 56°, because 124° + 56° = 180°. A 124° angle has no complement, because it is already larger than 90°.
How many radians is 124 degrees?
124° = 31π/45 radians ≈ 2.1642 rad. To convert degrees to radians, multiply by π/180: 124 × π/180 = 31π/45.
How do I measure a 124° angle on my screen?
Open the online protractor with 124° preset, or type 124 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
