A 252° 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 108° angle: together they make a full 360° circle.
252° is 7/10 of a full circle, or 7π/5 radians. The minute hand of a clock sweeps 252° in 42 minutes. If you face north and turn 252° clockwise, you end up facing between WSW and W (closest to west-southwest (WSW)).
252° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 108° |
| Radians | 7π/5 ≈ 4.39823 |
| Gradians | 280 grad |
| Fraction of a turn | 7/10 (70%) |
| Degrees, minutes, seconds | 252° 0′ 0″ |
| Compass bearing | between WSW and W (closest to west-southwest (WSW)) |
Trigonometric values of 252°
| Function | Value |
|---|---|
| sin 252° | −√(10 + 2√5)/4 ≈ −0.951057 |
| cos 252° | −(√5 − 1)/4 ≈ −0.309017 |
| tan 252° | 3.077684 |
252° on a protractor
How to draw a 252° angle with a protractor
- Subtract from 360°: 360° − 252° = 108°. 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 108°.
- Join the vertex to the dot. The inside angle is 108°; the outside angle, going the long way around, is 252°. Draw the angle arc on the outside and label it 252°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 252° directly.
Drawing it a 252° angle without a protractor (rise and run method)
- 252° = 180° − 72°. Draw a straight line, pick a vertex on it, and build a 72° angle on one side as follows; the angle on the other side of the new line is 108°.
- Draw a straight baseline and measure 3.25 inches (about 3 1/4″) 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 72°, because tan 72° ≈ 3.0777.
- That gives you 108°. The outside (reflex) angle is 252°.
Where you see 252° angles
- The Earth turns 252° on its axis in about 16 h 48 min.
- A 252° 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
252° angle FAQ
What type of angle is 252°?
A 252° angle is a reflex angle, because it is between 180° and 360°.
Does a 252° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 252° is already larger than both. What it does have is an explement (conjugate) of 108°, the angle that completes a full 360° circle.
How many radians is 252 degrees?
252° = 7π/5 radians ≈ 4.3982 rad. To convert degrees to radians, multiply by π/180: 252 × π/180 = 7π/5.
How do I measure a 252° angle on my screen?
Open the online protractor with 252° preset, or type 252 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
