A 198° 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 162° angle: together they make a full 360° circle.
198° is 11/20 of a full circle, or 11π/10 radians. The minute hand of a clock sweeps 198° in 33 minutes. If you face north and turn 198° clockwise, you end up facing between S and SSW (closest to south-southwest (SSW)).
198° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 162° |
| Radians | 11π/10 ≈ 3.455752 |
| Gradians | 220 grad |
| Fraction of a turn | 11/20 (55%) |
| Degrees, minutes, seconds | 198° 0′ 0″ |
| Compass bearing | between S and SSW (closest to south-southwest (SSW)) |
Trigonometric values of 198°
| Function | Value |
|---|---|
| sin 198° | −(√5 − 1)/4 ≈ −0.309017 |
| cos 198° | −√(10 + 2√5)/4 ≈ −0.951057 |
| tan 198° | 0.32492 |
198° on a protractor
How to draw a 198° angle with a protractor
- Subtract from 360°: 360° − 198° = 162°. 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 162°.
- Join the vertex to the dot. The inside angle is 162°; the outside angle, going the long way around, is 198°. Draw the angle arc on the outside and label it 198°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 198° directly.
Drawing it a 198° angle without a protractor (rise and run method)
- 198° = 180° − 18°. Draw a straight line, pick a vertex on it, and build an 18° angle on one side as follows; the angle on the other side of the new line is 162°.
- 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 3.25 inches (about 3 1/4″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 18°, because tan 18° ≈ 0.3249.
- That gives you 162°. The outside (reflex) angle is 198°.
Where you see 198° angles
- The Earth turns 198° on its axis in about 13 h 12 min.
- A 198° 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
198° angle FAQ
What type of angle is 198°?
A 198° angle is a reflex angle, because it is between 180° and 360°.
Does a 198° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 198° is already larger than both. What it does have is an explement (conjugate) of 162°, the angle that completes a full 360° circle.
How many radians is 198 degrees?
198° = 11π/10 radians ≈ 3.4558 rad. To convert degrees to radians, multiply by π/180: 198 × π/180 = 11π/10.
How do I measure a 198° angle on my screen?
Open the online protractor with 198° preset, or type 198 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
