A 243° 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 117° angle: together they make a full 360° circle.
243° is 27/40 of a full circle, or 27π/20 radians. If you face north and turn 243° clockwise, you end up facing between SW and WSW (closest to west-southwest (WSW)).
243° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 117° |
| Radians | 27π/20 ≈ 4.24115 |
| Gradians | 270 grad |
| Fraction of a turn | 27/40 (67.5%) |
| Degrees, minutes, seconds | 243° 0′ 0″ |
| Compass bearing | between SW and WSW (closest to west-southwest (WSW)) |
Trigonometric values of 243°
| Function | Value |
|---|---|
| sin 243° | −0.891007 |
| cos 243° | −0.45399 |
| tan 243° | 1.962611 |
243° on a protractor
How to draw a 243° angle with a protractor
- Subtract from 360°: 360° − 243° = 117°. 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 117°.
- Join the vertex to the dot. The inside angle is 117°; the outside angle, going the long way around, is 243°. Draw the angle arc on the outside and label it 243°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 243° directly.
Drawing it a 243° angle without a protractor (rise and run method)
- 243° = 180° − 63°. Draw a straight line, pick a vertex on it, and build a 63° angle on one side as follows; the angle on the other side of the new line is 117°.
- Draw a straight baseline and measure 5.1 inches (about 5 1/8″) 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 63°, because tan 63° ≈ 1.9626.
- That gives you 117°. The outside (reflex) angle is 243°.
Where you see 243° angles
- The Earth turns 243° on its axis in about 16 h 12 min.
- A 243° 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
243° angle FAQ
What type of angle is 243°?
A 243° angle is a reflex angle, because it is between 180° and 360°.
Does a 243° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 243° is already larger than both. What it does have is an explement (conjugate) of 117°, the angle that completes a full 360° circle.
How many radians is 243 degrees?
243° = 27π/20 radians ≈ 4.2412 rad. To convert degrees to radians, multiply by π/180: 243 × π/180 = 27π/20.
How do I measure a 243° angle on my screen?
Open the online protractor with 243° preset, or type 243 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
