A 191° angle is reflex because it measures between 180° and 360°. It is the "outside" of a 169° angle: together they make a full 360° circle.
191° is 191/360 of a full circle, or 191π/180 radians. If you face north and turn 191° clockwise, you end up facing between S and SSW (closest to south (S)).
191° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 169° |
| Radians | 191π/180 ≈ 3.333579 |
| Gradians | 212.2222 grad |
| Fraction of a turn | 191/360 (53.06%) |
| Degrees, minutes, seconds | 191° 0′ 0″ |
| Compass bearing | between S and SSW (closest to south (S)) |
Trigonometric values of 191°
| Function | Value |
|---|---|
| sin 191° | −0.190809 |
| cos 191° | −0.981627 |
| tan 191° | 0.19438 |
191° on a protractor
How to draw a 191° angle with a protractor
- Subtract from 360°: 360° − 191° = 169°. 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 169°.
- Join the vertex to the dot. The inside angle is 169°; the outside angle, going the long way around, is 191°. Draw the angle arc on the outside and label it 191°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 191° directly.
Drawing it a 191° angle without a protractor (rise and run method)
- 191° = 180° − 11°. Draw a straight line, pick a vertex on it, and build an 11° angle on one side as follows; the angle on the other side of the new line is 169°.
- Draw a straight baseline and measure exactly 10 inches along it from the vertex.
- At the 10-inch mark, draw a short line straight up at 90° (use a carpenter's square or the corner of a sheet of paper).
- Measure 1.94 inches (about 1 15/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 11°, because tan 11° ≈ 0.1944.
- That gives you 169°. The outside (reflex) angle is 191°.
Where you see 191° angles
- The Earth turns 191° on its axis in about 12 h 44 min.
- A 191° 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
191° angle FAQ
What type of angle is 191°?
A 191° angle is a reflex angle, because it is between 180° and 360°.
Does a 191° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 191° is already larger than both. What it does have is an explement (conjugate) of 169°, the angle that completes a full 360° circle.
How many radians is 191 degrees?
191° = 191π/180 radians ≈ 3.3336 rad. To convert degrees to radians, multiply by π/180: 191 × π/180 = 191π/180.
How do I measure a 191° angle on my screen?
Open the online protractor with 191° preset, or type 191 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
