A 291° 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 69° angle: together they make a full 360° circle.
291° is 97/120 of a full circle, or 97π/60 radians. If you face north and turn 291° clockwise, you end up facing between W and WNW (closest to west-northwest (WNW)).
291° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 69° |
| Radians | 97π/60 ≈ 5.078908 |
| Gradians | 323.3333 grad |
| Fraction of a turn | 97/120 (80.83%) |
| Degrees, minutes, seconds | 291° 0′ 0″ |
| Compass bearing | between W and WNW (closest to west-northwest (WNW)) |
Trigonometric values of 291°
| Function | Value |
|---|---|
| sin 291° | −0.93358 |
| cos 291° | 0.358368 |
| tan 291° | −2.605089 |
291° on a protractor
How to draw a 291° angle with a protractor
- Subtract from 360°: 360° − 291° = 69°. 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 69°.
- Join the vertex to the dot. The inside angle is 69°; the outside angle, going the long way around, is 291°. Draw the angle arc on the outside and label it 291°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 291° directly.
Drawing it a 291° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 3.84 inches (about 3 13/16″) 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 69°, because tan 69° ≈ 2.6051.
- That gives you 69°. The outside (reflex) angle is 291°.
Where you see 291° angles
- The Earth turns 291° on its axis in about 19 h 24 min.
- A 291° 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
291° angle FAQ
What type of angle is 291°?
A 291° angle is a reflex angle, because it is between 180° and 360°.
Does a 291° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 291° is already larger than both. What it does have is an explement (conjugate) of 69°, the angle that completes a full 360° circle.
How many radians is 291 degrees?
291° = 97π/60 radians ≈ 5.0789 rad. To convert degrees to radians, multiply by π/180: 291 × π/180 = 97π/60.
How do I measure a 291° angle on my screen?
Open the online protractor with 291° preset, or type 291 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
