A 107° angle is obtuse because it is greater than 90° and less than 180°. Its supplement is 73°, so a 107° angle and a 73° angle side by side make a straight line.
107° is 107/360 of a full circle, or 107π/180 radians. If you face north and turn 107° clockwise, you end up facing between E and ESE (closest to east-southeast (ESE)).
107° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 73° |
| Explement (adds to 360°) | 253° |
| Radians | 107π/180 ≈ 1.867502 |
| Gradians | 118.8889 grad |
| Fraction of a turn | 107/360 (29.72%) |
| Degrees, minutes, seconds | 107° 0′ 0″ |
| Compass bearing | between E and ESE (closest to east-southeast (ESE)) |
Trigonometric values of 107°
| Function | Value |
|---|---|
| sin 107° | 0.956305 |
| cos 107° | −0.292372 |
| tan 107° | −3.270853 |
107° on a protractor
How to draw a 107° 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 107° 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 107°.
Drawing it a 107° angle without a protractor (rise and run method)
- 107° = 180° − 73°. Draw a straight line, pick a vertex on it, and build a 73° angle on one side as follows; the angle on the other side of the new line is 107°.
- Draw a straight baseline and measure 3.06 inches (about 3 1/16″) 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 73°, because tan 73° ≈ 3.2709.
Where you see 107° angles
- The Earth turns 107° on its axis in about 7 h 8 min.
- Obtuse angles like 107° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
107° angle FAQ
What type of angle is 107°?
A 107° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 107°?
The supplement of 107° is 73°, because 107° + 73° = 180°. A 107° angle has no complement, because it is already larger than 90°.
How many radians is 107 degrees?
107° = 107π/180 radians ≈ 1.8675 rad. To convert degrees to radians, multiply by π/180: 107 × π/180 = 107π/180.
How do I measure a 107° angle on my screen?
Open the online protractor with 107° preset, or type 107 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
