At 307°, this is a reflex angle, which goes more than halfway around a circle. It is the "outside" of a 53° angle: together they make a full 360° circle.
307° is 307/360 of a full circle, or 307π/180 radians. If you face north and turn 307° clockwise, you end up facing between WNW and NW (closest to northwest (NW)).
307° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 53° |
| Radians | 307π/180 ≈ 5.358161 |
| Gradians | 341.1111 grad |
| Fraction of a turn | 307/360 (85.28%) |
| Degrees, minutes, seconds | 307° 0′ 0″ |
| Compass bearing | between WNW and NW (closest to northwest (NW)) |
Trigonometric values of 307°
| Function | Value |
|---|---|
| sin 307° | −0.798636 |
| cos 307° | 0.601815 |
| tan 307° | −1.327045 |
307° on a protractor
How to draw a 307° angle with a protractor
- Subtract from 360°: 360° − 307° = 53°. 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 53°.
- Join the vertex to the dot. The inside angle is 53°; the outside angle, going the long way around, is 307°. Draw the angle arc on the outside and label it 307°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 307° directly.
Drawing it a 307° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 7.54 inches (about 7 9/16″) 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 53°, because tan 53° ≈ 1.327.
- That gives you 53°. The outside (reflex) angle is 307°.
Where you see 307° angles
- The Earth turns 307° on its axis in about 20 h 28 min.
- A 307° 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
307° angle FAQ
What type of angle is 307°?
A 307° angle is a reflex angle, because it is between 180° and 360°.
Does a 307° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 307° is already larger than both. What it does have is an explement (conjugate) of 53°, the angle that completes a full 360° circle.
How many radians is 307 degrees?
307° = 307π/180 radians ≈ 5.3582 rad. To convert degrees to radians, multiply by π/180: 307 × π/180 = 307π/180.
How do I measure a 307° angle on my screen?
Open the online protractor with 307° preset, or type 307 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
