At 175°, this is an obtuse angle, opened up past a square corner but not yet flat. Its supplement is 5°, so a 175° angle and a 5° angle side by side make a straight line.
175° is 35/72 of a full circle, or 35π/36 radians. If you face north and turn 175° clockwise, you end up facing between SSE and S (closest to south (S)).
175° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 5° |
| Explement (adds to 360°) | 185° |
| Radians | 35π/36 ≈ 3.054326 |
| Gradians | 194.4444 grad |
| Fraction of a turn | 35/72 (48.61%) |
| Degrees, minutes, seconds | 175° 0′ 0″ |
| Compass bearing | between SSE and S (closest to south (S)) |
Trigonometric values of 175°
| Function | Value |
|---|---|
| sin 175° | 0.087156 |
| cos 175° | −0.996195 |
| tan 175° | −0.087489 |
175° on a protractor
How to draw a 175° 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 175° 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 175°.
Drawing it a 175° angle without a protractor (rise and run method)
- 175° = 180° − 5°. Draw a straight line, pick a vertex on it, and build a 5° angle on one side as follows; the angle on the other side of the new line is 175°.
- 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 0.87 inches (about 7/8″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 5°, because tan 5° ≈ 0.0875.
Where you see 175° angles
- The Earth turns 175° on its axis in about 11 h 40 min.
- Obtuse angles like 175° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
175° angle FAQ
What type of angle is 175°?
A 175° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 175°?
The supplement of 175° is 5°, because 175° + 5° = 180°. A 175° angle has no complement, because it is already larger than 90°.
How many radians is 175 degrees?
175° = 35π/36 radians ≈ 3.0543 rad. To convert degrees to radians, multiply by π/180: 175 × π/180 = 35π/36.
How do I measure a 175° angle on my screen?
Open the online protractor with 175° preset, or type 175 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
