A 155° angle is obtuse because it is greater than 90° and less than 180°. Its supplement is 25°, so a 155° angle and a 25° angle side by side make a straight line.
155° is 31/72 of a full circle, or 31π/36 radians. If you face north and turn 155° clockwise, you end up facing between SE and SSE (closest to south-southeast (SSE)).
155° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 25° |
| Explement (adds to 360°) | 205° |
| Radians | 31π/36 ≈ 2.70526 |
| Gradians | 172.2222 grad |
| Fraction of a turn | 31/72 (43.06%) |
| Degrees, minutes, seconds | 155° 0′ 0″ |
| Compass bearing | between SE and SSE (closest to south-southeast (SSE)) |
Trigonometric values of 155°
| Function | Value |
|---|---|
| sin 155° | 0.422618 |
| cos 155° | −0.906308 |
| tan 155° | −0.466308 |
155° on a protractor
How to draw a 155° 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 155° 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 155°.
Drawing it a 155° angle without a protractor (rise and run method)
- 155° = 180° − 25°. Draw a straight line, pick a vertex on it, and build a 25° angle on one side as follows; the angle on the other side of the new line is 155°.
- 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 4.66 inches (about 4 11/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 25°, because tan 25° ≈ 0.4663.
Where you see 155° angles
- The Earth turns 155° on its axis in about 10 h 20 min.
- Obtuse angles like 155° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
155° angle FAQ
What type of angle is 155°?
A 155° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 155°?
The supplement of 155° is 25°, because 155° + 25° = 180°. A 155° angle has no complement, because it is already larger than 90°.
How many radians is 155 degrees?
155° = 31π/36 radians ≈ 2.7053 rad. To convert degrees to radians, multiply by π/180: 155 × π/180 = 31π/36.
How do I measure a 155° angle on my screen?
Open the online protractor with 155° preset, or type 155 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
