At 238°, this is a reflex angle, which goes more than halfway around a circle. It is the "outside" of a 122° angle: together they make a full 360° circle.
238° is 119/180 of a full circle, or 119π/90 radians. If you face north and turn 238° clockwise, you end up facing between SW and WSW (closest to west-southwest (WSW)).
238° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 122° |
| Radians | 119π/90 ≈ 4.153884 |
| Gradians | 264.4444 grad |
| Fraction of a turn | 119/180 (66.11%) |
| Degrees, minutes, seconds | 238° 0′ 0″ |
| Compass bearing | between SW and WSW (closest to west-southwest (WSW)) |
Trigonometric values of 238°
| Function | Value |
|---|---|
| sin 238° | −0.848048 |
| cos 238° | −0.529919 |
| tan 238° | 1.600335 |
238° on a protractor
How to draw a 238° angle with a protractor
- Subtract from 360°: 360° − 238° = 122°. 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 122°.
- Join the vertex to the dot. The inside angle is 122°; the outside angle, going the long way around, is 238°. Draw the angle arc on the outside and label it 238°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 238° directly.
Drawing it a 238° angle without a protractor (rise and run method)
- 238° = 180° − 58°. Draw a straight line, pick a vertex on it, and build a 58° angle on one side as follows; the angle on the other side of the new line is 122°.
- Draw a straight baseline and measure 6.25 inches (about 6 1/4″) 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 58°, because tan 58° ≈ 1.6003.
- That gives you 122°. The outside (reflex) angle is 238°.
Where you see 238° angles
- The Earth turns 238° on its axis in about 15 h 52 min.
- A 238° 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
238° angle FAQ
What type of angle is 238°?
A 238° angle is a reflex angle, because it is between 180° and 360°.
Does a 238° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 238° is already larger than both. What it does have is an explement (conjugate) of 122°, the angle that completes a full 360° circle.
How many radians is 238 degrees?
238° = 119π/90 radians ≈ 4.1539 rad. To convert degrees to radians, multiply by π/180: 238 × π/180 = 119π/90.
How do I measure a 238° angle on my screen?
Open the online protractor with 238° preset, or type 238 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
