A 140° angle is obtuse because it is greater than 90° and less than 180°. Its supplement is 40°, so a 140° angle and a 40° angle side by side make a straight line.
140° is 7/18 of a full circle, or 7π/9 radians. If you face north and turn 140° clockwise, you end up facing between SE and SSE (closest to southeast (SE)).
140° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 40° |
| Explement (adds to 360°) | 220° |
| Radians | 7π/9 ≈ 2.443461 |
| Gradians | 155.5556 grad |
| Fraction of a turn | 7/18 (38.89%) |
| Degrees, minutes, seconds | 140° 0′ 0″ |
| Compass bearing | between SE and SSE (closest to southeast (SE)) |
Trigonometric values of 140°
| Function | Value |
|---|---|
| sin 140° | 0.642788 |
| cos 140° | −0.766044 |
| tan 140° | −0.8391 |
140° on a protractor
How to draw a 140° 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 140° 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 140°.
Drawing it a 140° angle without a protractor (rise and run method)
- 140° = 180° − 40°. Draw a straight line, pick a vertex on it, and build a 40° angle on one side as follows; the angle on the other side of the new line is 140°.
- 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 8.39 inches (about 8 3/8″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 40°, because tan 40° ≈ 0.8391.
Where you see 140° angles
- Each interior corner of a regular nonagon measures 140°.
- The Earth turns 140° on its axis in about 9 h 20 min.
- Obtuse angles like 140° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
140° angle FAQ
What type of angle is 140°?
A 140° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 140°?
The supplement of 140° is 40°, because 140° + 40° = 180°. A 140° angle has no complement, because it is already larger than 90°.
How many radians is 140 degrees?
140° = 7π/9 radians ≈ 2.4435 rad. To convert degrees to radians, multiply by π/180: 140 × π/180 = 7π/9.
How do I measure a 140° angle on my screen?
Open the online protractor with 140° preset, or type 140 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
