A 105° angle is an obtuse angle: wider than a right angle (90°) but less than a straight line (180°). Its supplement is 75°, so a 105° angle and a 75° angle side by side make a straight line.
105° is 7/24 of a full circle, or 7π/12 radians. If you face north and turn 105° clockwise, you end up facing between E and ESE (closest to east-southeast (ESE)).
105° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 75° |
| Explement (adds to 360°) | 255° |
| Radians | 7π/12 ≈ 1.832596 |
| Gradians | 116.6667 grad |
| Fraction of a turn | 7/24 (29.17%) |
| Degrees, minutes, seconds | 105° 0′ 0″ |
| Compass bearing | between E and ESE (closest to east-southeast (ESE)) |
Trigonometric values of 105°
| Function | Value |
|---|---|
| sin 105° | (√6 + √2)/4 ≈ 0.965926 |
| cos 105° | −(√6 − √2)/4 ≈ −0.258819 |
| tan 105° | −(2 + √3) ≈ −3.732051 |
105° on a protractor
How to draw a 105° 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 105° 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 105°.
Drawing it a 105° angle without a protractor (compass and ruler)
- Draw a 90° angle: construct a perpendicular line (draw arcs from two points on the line and join their crossing points).
- Using the second arm as your new base, add a 15° angle on the outside: construct a 30° angle, then bisect it.
- The angle between the first arm and the new arm is 90° + 15° = 105°.
Where you see 105° angles
- The H–O–H bond angle of a water molecule is about 104.5°, just under 105°.
- The Earth turns 105° on its axis in about 7 hours.
- Obtuse angles like 105° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
105° angle FAQ
What type of angle is 105°?
A 105° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 105°?
The supplement of 105° is 75°, because 105° + 75° = 180°. A 105° angle has no complement, because it is already larger than 90°.
How many radians is 105 degrees?
105° = 7π/12 radians ≈ 1.8326 rad. To convert degrees to radians, multiply by π/180: 105 × π/180 = 7π/12.
How do I measure a 105° angle on my screen?
Open the online protractor with 105° preset, or type 105 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
