At 172°, this is an obtuse angle, opened up past a square corner but not yet flat. Its supplement is 8°, so a 172° angle and an 8° angle side by side make a straight line.
172° is 43/90 of a full circle, or 43π/45 radians. If you face north and turn 172° clockwise, you end up facing between SSE and S (closest to south (S)).
172° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 8° |
| Explement (adds to 360°) | 188° |
| Radians | 43π/45 ≈ 3.001966 |
| Gradians | 191.1111 grad |
| Fraction of a turn | 43/90 (47.78%) |
| Degrees, minutes, seconds | 172° 0′ 0″ |
| Compass bearing | between SSE and S (closest to south (S)) |
Trigonometric values of 172°
| Function | Value |
|---|---|
| sin 172° | 0.139173 |
| cos 172° | −0.990268 |
| tan 172° | −0.140541 |
172° on a protractor
How to draw a 172° 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 172° 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 172°.
Drawing it a 172° angle without a protractor (rise and run method)
- 172° = 180° − 8°. Draw a straight line, pick a vertex on it, and build an 8° angle on one side as follows; the angle on the other side of the new line is 172°.
- 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 1.41 inches (about 1 3/8″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 8°, because tan 8° ≈ 0.1405.
Where you see 172° angles
- Each interior corner of a regular 45-sided polygon measures 172°.
- The Earth turns 172° on its axis in about 11 h 28 min.
- Obtuse angles like 172° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
172° angle FAQ
What type of angle is 172°?
A 172° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 172°?
The supplement of 172° is 8°, because 172° + 8° = 180°. A 172° angle has no complement, because it is already larger than 90°.
How many radians is 172 degrees?
172° = 43π/45 radians ≈ 3.002 rad. To convert degrees to radians, multiply by π/180: 172 × π/180 = 43π/45.
How do I measure a 172° angle on my screen?
Open the online protractor with 172° preset, or type 172 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
