A 309° 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 51° angle: together they make a full 360° circle.
309° is 103/120 of a full circle, or 103π/60 radians. If you face north and turn 309° clockwise, you end up facing between WNW and NW (closest to northwest (NW)).
309° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 51° |
| Radians | 103π/60 ≈ 5.393067 |
| Gradians | 343.3333 grad |
| Fraction of a turn | 103/120 (85.83%) |
| Degrees, minutes, seconds | 309° 0′ 0″ |
| Compass bearing | between WNW and NW (closest to northwest (NW)) |
Trigonometric values of 309°
| Function | Value |
|---|---|
| sin 309° | −0.777146 |
| cos 309° | 0.62932 |
| tan 309° | −1.234897 |
309° on a protractor
How to draw a 309° angle with a protractor
- Subtract from 360°: 360° − 309° = 51°. 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 51°.
- Join the vertex to the dot. The inside angle is 51°; the outside angle, going the long way around, is 309°. Draw the angle arc on the outside and label it 309°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 309° directly.
Drawing it a 309° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 8.1 inches (about 8 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 51°, because tan 51° ≈ 1.2349.
- That gives you 51°. The outside (reflex) angle is 309°.
Where you see 309° angles
- The Earth turns 309° on its axis in about 20 h 36 min.
- A 309° 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
309° angle FAQ
What type of angle is 309°?
A 309° angle is a reflex angle, because it is between 180° and 360°.
Does a 309° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 309° is already larger than both. What it does have is an explement (conjugate) of 51°, the angle that completes a full 360° circle.
How many radians is 309 degrees?
309° = 103π/60 radians ≈ 5.3931 rad. To convert degrees to radians, multiply by π/180: 309 × π/180 = 103π/60.
How do I measure a 309° angle on my screen?
Open the online protractor with 309° preset, or type 309 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
