A 228° angle is a reflex angle: it is bigger than a straight line (180°) but less than a full turn (360°). It is the "outside" of a 132° angle: together they make a full 360° circle.
228° is 19/30 of a full circle, or 19π/15 radians. The minute hand of a clock sweeps 228° in 38 minutes. If you face north and turn 228° clockwise, you end up facing between SW and WSW (closest to southwest (SW)).
228° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 132° |
| Radians | 19π/15 ≈ 3.979351 |
| Gradians | 253.3333 grad |
| Fraction of a turn | 19/30 (63.33%) |
| Degrees, minutes, seconds | 228° 0′ 0″ |
| Compass bearing | between SW and WSW (closest to southwest (SW)) |
Trigonometric values of 228°
| Function | Value |
|---|---|
| sin 228° | −0.743145 |
| cos 228° | −0.669131 |
| tan 228° | 1.110613 |
228° on a protractor
How to draw a 228° angle with a protractor
- Subtract from 360°: 360° − 228° = 132°. 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 132°.
- Join the vertex to the dot. The inside angle is 132°; the outside angle, going the long way around, is 228°. Draw the angle arc on the outside and label it 228°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 228° directly.
Drawing it a 228° angle without a protractor (rise and run method)
- 228° = 180° − 48°. Draw a straight line, pick a vertex on it, and build a 48° angle on one side as follows; the angle on the other side of the new line is 132°.
- Draw a straight baseline and measure 9 inches (about 9″) 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 48°, because tan 48° ≈ 1.1106.
- That gives you 132°. The outside (reflex) angle is 228°.
Where you see 228° angles
- The Earth turns 228° on its axis in about 15 h 12 min.
- A 228° 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
228° angle FAQ
What type of angle is 228°?
A 228° angle is a reflex angle, because it is between 180° and 360°.
Does a 228° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 228° is already larger than both. What it does have is an explement (conjugate) of 132°, the angle that completes a full 360° circle.
How many radians is 228 degrees?
228° = 19π/15 radians ≈ 3.9794 rad. To convert degrees to radians, multiply by π/180: 228 × π/180 = 19π/15.
How do I measure a 228° angle on my screen?
Open the online protractor with 228° preset, or type 228 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
