A 189° 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 171° angle: together they make a full 360° circle.
189° is 21/40 of a full circle, or 21π/20 radians. If you face north and turn 189° clockwise, you end up facing between S and SSW (closest to south (S)).
189° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 171° |
| Radians | 21π/20 ≈ 3.298672 |
| Gradians | 210 grad |
| Fraction of a turn | 21/40 (52.5%) |
| Degrees, minutes, seconds | 189° 0′ 0″ |
| Compass bearing | between S and SSW (closest to south (S)) |
Trigonometric values of 189°
| Function | Value |
|---|---|
| sin 189° | −0.156434 |
| cos 189° | −0.987688 |
| tan 189° | 0.158384 |
189° on a protractor
How to draw a 189° angle with a protractor
- Subtract from 360°: 360° − 189° = 171°. 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 171°.
- Join the vertex to the dot. The inside angle is 171°; the outside angle, going the long way around, is 189°. Draw the angle arc on the outside and label it 189°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 189° directly.
Drawing it a 189° angle without a protractor (rise and run method)
- 189° = 180° − 9°. Draw a straight line, pick a vertex on it, and build a 9° angle on one side as follows; the angle on the other side of the new line is 171°.
- 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 1.58 inches (about 1 9/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 9°, because tan 9° ≈ 0.1584.
- That gives you 171°. The outside (reflex) angle is 189°.
Where you see 189° angles
- The Earth turns 189° on its axis in about 12 h 36 min.
- A 189° 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
189° angle FAQ
What type of angle is 189°?
A 189° angle is a reflex angle, because it is between 180° and 360°.
Does a 189° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 189° is already larger than both. What it does have is an explement (conjugate) of 171°, the angle that completes a full 360° circle.
How many radians is 189 degrees?
189° = 21π/20 radians ≈ 3.2987 rad. To convert degrees to radians, multiply by π/180: 189 × π/180 = 21π/20.
How do I measure a 189° angle on my screen?
Open the online protractor with 189° preset, or type 189 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
