A 165° angle is an obtuse angle: wider than a right angle (90°) but less than a straight line (180°). Its supplement is 15°, so a 165° angle and a 15° angle side by side make a straight line.
165° is 11/24 of a full circle, or 11π/12 radians. If you face north and turn 165° clockwise, you end up facing between SSE and S (closest to south-southeast (SSE)).
165° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 15° |
| Explement (adds to 360°) | 195° |
| Radians | 11π/12 ≈ 2.879793 |
| Gradians | 183.3333 grad |
| Fraction of a turn | 11/24 (45.83%) |
| Degrees, minutes, seconds | 165° 0′ 0″ |
| Compass bearing | between SSE and S (closest to south-southeast (SSE)) |
Trigonometric values of 165°
| Function | Value |
|---|---|
| sin 165° | (√6 − √2)/4 ≈ 0.258819 |
| cos 165° | −(√6 + √2)/4 ≈ −0.965926 |
| tan 165° | −(2 − √3) ≈ −0.267949 |
165° on a protractor
How to draw a 165° 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 165° 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 165°.
Drawing it a 165° angle without a protractor (compass and ruler)
- Draw a 180° angle: draw a straight line.
- Inside it, starting from the second arm, mark a 15° angle: construct a 30° angle, then bisect it.
- What is left between the first arm and the new line is 180° − 15° = 165°.
Where you see 165° angles
- Each interior corner of a regular 24-sided polygon measures 165°.
- The Earth turns 165° on its axis in about 11 hours.
- Obtuse angles like 165° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
165° angle FAQ
What type of angle is 165°?
A 165° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 165°?
The supplement of 165° is 15°, because 165° + 15° = 180°. A 165° angle has no complement, because it is already larger than 90°.
How many radians is 165 degrees?
165° = 11π/12 radians ≈ 2.8798 rad. To convert degrees to radians, multiply by π/180: 165 × π/180 = 11π/12.
How do I measure a 165° angle on my screen?
Open the online protractor with 165° preset, or type 165 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
