A 345° 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 15° angle: together they make a full 360° circle.
345° is 23/24 of a full circle, or 23π/12 radians. If you face north and turn 345° clockwise, you end up facing between NNW and N (closest to north-northwest (NNW)).
345° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 15° |
| Radians | 23π/12 ≈ 6.021386 |
| Gradians | 383.3333 grad |
| Fraction of a turn | 23/24 (95.83%) |
| Degrees, minutes, seconds | 345° 0′ 0″ |
| Compass bearing | between NNW and N (closest to north-northwest (NNW)) |
Trigonometric values of 345°
| Function | Value |
|---|---|
| sin 345° | −(√6 − √2)/4 ≈ −0.258819 |
| cos 345° | (√6 + √2)/4 ≈ 0.965926 |
| tan 345° | −(2 − √3) ≈ −0.267949 |
345° on a protractor
How to draw a 345° angle with a protractor
- Subtract from 360°: 360° − 345° = 15°. 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 15°.
- Join the vertex to the dot. The inside angle is 15°; the outside angle, going the long way around, is 345°. Draw the angle arc on the outside and label it 345°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 345° directly.
Drawing it a 345° angle without a protractor (compass and ruler)
- Construct a 30° angle, then bisect it.
- That gives you 15°. The reflex angle on the outside of it is 345°.
Where you see 345° angles
- The Earth turns 345° on its axis in about 23 hours.
- A 345° 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
345° angle FAQ
What type of angle is 345°?
A 345° angle is a reflex angle, because it is between 180° and 360°.
Does a 345° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 345° is already larger than both. What it does have is an explement (conjugate) of 15°, the angle that completes a full 360° circle.
How many radians is 345 degrees?
345° = 23π/12 radians ≈ 6.0214 rad. To convert degrees to radians, multiply by π/180: 345 × π/180 = 23π/12.
How do I measure a 345° angle on my screen?
Open the online protractor with 345° preset, or type 345 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
