A 224° angle is reflex because it measures between 180° and 360°. It is the "outside" of a 136° angle: together they make a full 360° circle.
224° is 28/45 of a full circle, or 56π/45 radians. If you face north and turn 224° clockwise, you end up facing between SSW and SW (closest to southwest (SW)).
224° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 136° |
| Radians | 56π/45 ≈ 3.909538 |
| Gradians | 248.8889 grad |
| Fraction of a turn | 28/45 (62.22%) |
| Degrees, minutes, seconds | 224° 0′ 0″ |
| Compass bearing | between SSW and SW (closest to southwest (SW)) |
Trigonometric values of 224°
| Function | Value |
|---|---|
| sin 224° | −0.694658 |
| cos 224° | −0.71934 |
| tan 224° | 0.965689 |
224° on a protractor
How to draw a 224° angle with a protractor
- Subtract from 360°: 360° − 224° = 136°. 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 136°.
- Join the vertex to the dot. The inside angle is 136°; the outside angle, going the long way around, is 224°. Draw the angle arc on the outside and label it 224°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 224° directly.
Drawing it a 224° angle without a protractor (rise and run method)
- 224° = 180° − 44°. Draw a straight line, pick a vertex on it, and build a 44° angle on one side as follows; the angle on the other side of the new line is 136°.
- 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 9.66 inches (about 9 11/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 44°, because tan 44° ≈ 0.9657.
- That gives you 136°. The outside (reflex) angle is 224°.
Where you see 224° angles
- The Earth turns 224° on its axis in about 14 h 56 min.
- A 224° 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
224° angle FAQ
What type of angle is 224°?
A 224° angle is a reflex angle, because it is between 180° and 360°.
Does a 224° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 224° is already larger than both. What it does have is an explement (conjugate) of 136°, the angle that completes a full 360° circle.
How many radians is 224 degrees?
224° = 56π/45 radians ≈ 3.9095 rad. To convert degrees to radians, multiply by π/180: 224 × π/180 = 56π/45.
How do I measure a 224° angle on my screen?
Open the online protractor with 224° preset, or type 224 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
