At 202°, this is a reflex angle, which goes more than halfway around a circle. It is the "outside" of a 158° angle: together they make a full 360° circle.
202° is 101/180 of a full circle, or 101π/90 radians. If you face north and turn 202° clockwise, you end up facing between S and SSW (closest to south-southwest (SSW)).
202° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 158° |
| Radians | 101π/90 ≈ 3.525565 |
| Gradians | 224.4444 grad |
| Fraction of a turn | 101/180 (56.11%) |
| Degrees, minutes, seconds | 202° 0′ 0″ |
| Compass bearing | between S and SSW (closest to south-southwest (SSW)) |
Trigonometric values of 202°
| Function | Value |
|---|---|
| sin 202° | −0.374607 |
| cos 202° | −0.927184 |
| tan 202° | 0.404026 |
202° on a protractor
How to draw a 202° angle with a protractor
- Subtract from 360°: 360° − 202° = 158°. 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 158°.
- Join the vertex to the dot. The inside angle is 158°; the outside angle, going the long way around, is 202°. Draw the angle arc on the outside and label it 202°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 202° directly.
Drawing it a 202° angle without a protractor (rise and run method)
- 202° = 180° − 22°. Draw a straight line, pick a vertex on it, and build a 22° angle on one side as follows; the angle on the other side of the new line is 158°.
- 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 4.04 inches (about 4 1/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 22°, because tan 22° ≈ 0.404.
- That gives you 158°. The outside (reflex) angle is 202°.
Where you see 202° angles
- The Earth turns 202° on its axis in about 13 h 28 min.
- A 202° 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
202° angle FAQ
What type of angle is 202°?
A 202° angle is a reflex angle, because it is between 180° and 360°.
Does a 202° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 202° is already larger than both. What it does have is an explement (conjugate) of 158°, the angle that completes a full 360° circle.
How many radians is 202 degrees?
202° = 101π/90 radians ≈ 3.5256 rad. To convert degrees to radians, multiply by π/180: 202 × π/180 = 101π/90.
How do I measure a 202° angle on my screen?
Open the online protractor with 202° preset, or type 202 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
