A 177° angle is an obtuse angle: wider than a right angle (90°) but less than a straight line (180°). Its supplement is 3°, so a 177° angle and a 3° angle side by side make a straight line.
177° is 59/120 of a full circle, or 59π/60 radians. If you face north and turn 177° clockwise, you end up facing between SSE and S (closest to south (S)).
177° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 3° |
| Explement (adds to 360°) | 183° |
| Radians | 59π/60 ≈ 3.089233 |
| Gradians | 196.6667 grad |
| Fraction of a turn | 59/120 (49.17%) |
| Degrees, minutes, seconds | 177° 0′ 0″ |
| Compass bearing | between SSE and S (closest to south (S)) |
Trigonometric values of 177°
| Function | Value |
|---|---|
| sin 177° | 0.052336 |
| cos 177° | −0.99863 |
| tan 177° | −0.052408 |
177° on a protractor
How to draw a 177° 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 177° 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 177°.
Drawing it a 177° angle without a protractor (rise and run method)
- 177° = 180° − 3°. Draw a straight line, pick a vertex on it, and build a 3° angle on one side as follows; the angle on the other side of the new line is 177°.
- 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 0.52 inches (about 1/2″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 3°, because tan 3° ≈ 0.0524.
Where you see 177° angles
- The Earth turns 177° on its axis in about 11 h 48 min.
- Obtuse angles like 177° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
177° angle FAQ
What type of angle is 177°?
A 177° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 177°?
The supplement of 177° is 3°, because 177° + 3° = 180°. A 177° angle has no complement, because it is already larger than 90°.
How many radians is 177 degrees?
177° = 59π/60 radians ≈ 3.0892 rad. To convert degrees to radians, multiply by π/180: 177 × π/180 = 59π/60.
How do I measure a 177° angle on my screen?
Open the online protractor with 177° preset, or type 177 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
