A 138° angle is an obtuse angle: wider than a right angle (90°) but less than a straight line (180°). Its supplement is 42°, so a 138° angle and a 42° angle side by side make a straight line.
138° is 23/60 of a full circle, or 23π/30 radians. The minute hand of a clock sweeps 138° in 23 minutes. If you face north and turn 138° clockwise, you end up facing between SE and SSE (closest to southeast (SE)).
138° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 42° |
| Explement (adds to 360°) | 222° |
| Radians | 23π/30 ≈ 2.408554 |
| Gradians | 153.3333 grad |
| Fraction of a turn | 23/60 (38.33%) |
| Degrees, minutes, seconds | 138° 0′ 0″ |
| Compass bearing | between SE and SSE (closest to southeast (SE)) |
Trigonometric values of 138°
| Function | Value |
|---|---|
| sin 138° | 0.669131 |
| cos 138° | −0.743145 |
| tan 138° | −0.900404 |
138° on a protractor
How to draw a 138° 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 138° 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 138°.
Drawing it a 138° angle without a protractor (rise and run method)
- 138° = 180° − 42°. Draw a straight line, pick a vertex on it, and build a 42° angle on one side as follows; the angle on the other side of the new line is 138°.
- Draw a straight baseline and measure exactly 10 inches along it from the vertex.
- At the 10-inch mark, draw a short line straight up at 90° (use a carpenter's square or the corner of a sheet of paper).
- Measure 9 inches (about 9″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 42°, because tan 42° ≈ 0.9004.
Where you see 138° angles
- The Earth turns 138° on its axis in about 9 h 12 min.
- Obtuse angles like 138° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
138° angle FAQ
What type of angle is 138°?
A 138° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 138°?
The supplement of 138° is 42°, because 138° + 42° = 180°. A 138° angle has no complement, because it is already larger than 90°.
How many radians is 138 degrees?
138° = 23π/30 radians ≈ 2.4086 rad. To convert degrees to radians, multiply by π/180: 138 × π/180 = 23π/30.
How do I measure a 138° angle on my screen?
Open the online protractor with 138° preset, or type 138 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
