At 178°, this is an obtuse angle, opened up past a square corner but not yet flat. Its supplement is 2°, so a 178° angle and a 2° angle side by side make a straight line.
178° is 89/180 of a full circle, or 89π/90 radians. If you face north and turn 178° clockwise, you end up facing between SSE and S (closest to south (S)).
178° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 2° |
| Explement (adds to 360°) | 182° |
| Radians | 89π/90 ≈ 3.106686 |
| Gradians | 197.7778 grad |
| Fraction of a turn | 89/180 (49.44%) |
| Degrees, minutes, seconds | 178° 0′ 0″ |
| Compass bearing | between SSE and S (closest to south (S)) |
Trigonometric values of 178°
| Function | Value |
|---|---|
| sin 178° | 0.034899 |
| cos 178° | −0.999391 |
| tan 178° | −0.034921 |
178° on a protractor
How to draw a 178° 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 178° 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 178°.
Drawing it a 178° angle without a protractor (rise and run method)
- 178° = 180° − 2°. Draw a straight line, pick a vertex on it, and build a 2° angle on one side as follows; the angle on the other side of the new line is 178°.
- 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 0.35 inches (about 3/8″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 2°, because tan 2° ≈ 0.0349.
Where you see 178° angles
- The Earth turns 178° on its axis in about 11 h 52 min.
- Obtuse angles like 178° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
178° angle FAQ
What type of angle is 178°?
A 178° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 178°?
The supplement of 178° is 2°, because 178° + 2° = 180°. A 178° angle has no complement, because it is already larger than 90°.
How many radians is 178 degrees?
178° = 89π/90 radians ≈ 3.1067 rad. To convert degrees to radians, multiply by π/180: 178 × π/180 = 89π/90.
How do I measure a 178° angle on my screen?
Open the online protractor with 178° preset, or type 178 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
