A 258° 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 102° angle: together they make a full 360° circle.
258° is 43/60 of a full circle, or 43π/30 radians. The minute hand of a clock sweeps 258° in 43 minutes. If you face north and turn 258° clockwise, you end up facing between WSW and W (closest to west-southwest (WSW)).
258° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 102° |
| Radians | 43π/30 ≈ 4.502949 |
| Gradians | 286.6667 grad |
| Fraction of a turn | 43/60 (71.67%) |
| Degrees, minutes, seconds | 258° 0′ 0″ |
| Compass bearing | between WSW and W (closest to west-southwest (WSW)) |
Trigonometric values of 258°
| Function | Value |
|---|---|
| sin 258° | −0.978148 |
| cos 258° | −0.207912 |
| tan 258° | 4.70463 |
258° on a protractor
How to draw a 258° angle with a protractor
- Subtract from 360°: 360° − 258° = 102°. 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 102°.
- Join the vertex to the dot. The inside angle is 102°; the outside angle, going the long way around, is 258°. Draw the angle arc on the outside and label it 258°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 258° directly.
Drawing it a 258° angle without a protractor (rise and run method)
- 258° = 180° − 78°. Draw a straight line, pick a vertex on it, and build a 78° angle on one side as follows; the angle on the other side of the new line is 102°.
- Draw a straight baseline and measure 2.13 inches (about 2 1/8″) 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 78°, because tan 78° ≈ 4.7046.
- That gives you 102°. The outside (reflex) angle is 258°.
Where you see 258° angles
- The Earth turns 258° on its axis in about 17 h 12 min.
- A 258° 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
258° angle FAQ
What type of angle is 258°?
A 258° angle is a reflex angle, because it is between 180° and 360°.
Does a 258° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 258° is already larger than both. What it does have is an explement (conjugate) of 102°, the angle that completes a full 360° circle.
How many radians is 258 degrees?
258° = 43π/30 radians ≈ 4.5029 rad. To convert degrees to radians, multiply by π/180: 258 × π/180 = 43π/30.
How do I measure a 258° angle on my screen?
Open the online protractor with 258° preset, or type 258 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
