At 232°, this is a reflex angle, which goes more than halfway around a circle. It is the "outside" of a 128° angle: together they make a full 360° circle.
232° is 29/45 of a full circle, or 58π/45 radians. If you face north and turn 232° clockwise, you end up facing between SW and WSW (closest to southwest (SW)).
232° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 128° |
| Radians | 58π/45 ≈ 4.049164 |
| Gradians | 257.7778 grad |
| Fraction of a turn | 29/45 (64.44%) |
| Degrees, minutes, seconds | 232° 0′ 0″ |
| Compass bearing | between SW and WSW (closest to southwest (SW)) |
Trigonometric values of 232°
| Function | Value |
|---|---|
| sin 232° | −0.788011 |
| cos 232° | −0.615661 |
| tan 232° | 1.279942 |
232° on a protractor
How to draw a 232° angle with a protractor
- Subtract from 360°: 360° − 232° = 128°. A standard protractor only goes to 180°, so you draw the smaller angle first.
- Draw a straight line with a ruler and mark the vertex at one end.
- Place the protractor's center mark on the vertex, line up the 0° baseline with your line, and make a dot at 128°.
- Join the vertex to the dot. The inside angle is 128°; the outside angle, going the long way around, is 232°. Draw the angle arc on the outside and label it 232°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 232° directly.
Drawing it a 232° angle without a protractor (rise and run method)
- 232° = 180° − 52°. Draw a straight line, pick a vertex on it, and build a 52° angle on one side as follows; the angle on the other side of the new line is 128°.
- Draw a straight baseline and measure 7.81 inches (about 7 13/16″) along it from the vertex.
- At that mark, draw a line straight up at 90° and measure exactly 10 inches up it.
- Join the top mark to the vertex. The angle at the vertex is 52°, because tan 52° ≈ 1.2799.
- That gives you 128°. The outside (reflex) angle is 232°.
Where you see 232° angles
- The Earth turns 232° on its axis in about 15 h 28 min.
- A 232° reflex angle is what you measure when you go the "long way" around, like the outside corner of a building or a turn of more than half a circle.
Related angles
232° angle FAQ
What type of angle is 232°?
A 232° angle is a reflex angle, because it is between 180° and 360°.
Does a 232° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 232° is already larger than both. What it does have is an explement (conjugate) of 128°, the angle that completes a full 360° circle.
How many radians is 232 degrees?
232° = 58π/45 radians ≈ 4.0492 rad. To convert degrees to radians, multiply by π/180: 232 × π/180 = 58π/45.
How do I measure a 232° angle on my screen?
Open the online protractor with 232° preset, or type 232 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
