A 305° angle is reflex because it measures between 180° and 360°. It is the "outside" of a 55° angle: together they make a full 360° circle.
305° is 61/72 of a full circle, or 61π/36 radians. If you face north and turn 305° clockwise, you end up facing between WNW and NW (closest to northwest (NW)).
305° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 55° |
| Radians | 61π/36 ≈ 5.323254 |
| Gradians | 338.8889 grad |
| Fraction of a turn | 61/72 (84.72%) |
| Degrees, minutes, seconds | 305° 0′ 0″ |
| Compass bearing | between WNW and NW (closest to northwest (NW)) |
Trigonometric values of 305°
| Function | Value |
|---|---|
| sin 305° | −0.819152 |
| cos 305° | 0.573576 |
| tan 305° | −1.428148 |
305° on a protractor
How to draw a 305° angle with a protractor
- Subtract from 360°: 360° − 305° = 55°. 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 55°.
- Join the vertex to the dot. The inside angle is 55°; the outside angle, going the long way around, is 305°. Draw the angle arc on the outside and label it 305°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 305° directly.
Drawing it a 305° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 7 inches (about 7″) 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 55°, because tan 55° ≈ 1.4281.
- That gives you 55°. The outside (reflex) angle is 305°.
Where you see 305° angles
- The Earth turns 305° on its axis in about 20 h 20 min.
- A 305° 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
305° angle FAQ
What type of angle is 305°?
A 305° angle is a reflex angle, because it is between 180° and 360°.
Does a 305° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 305° is already larger than both. What it does have is an explement (conjugate) of 55°, the angle that completes a full 360° circle.
How many radians is 305 degrees?
305° = 61π/36 radians ≈ 5.3233 rad. To convert degrees to radians, multiply by π/180: 305 × π/180 = 61π/36.
How do I measure a 305° angle on my screen?
Open the online protractor with 305° preset, or type 305 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
