A 234° 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 126° angle: together they make a full 360° circle.
234° is 13/20 of a full circle, or 13π/10 radians. The minute hand of a clock sweeps 234° in 39 minutes. If you face north and turn 234° clockwise, you end up facing between SW and WSW (closest to southwest (SW)).
234° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 126° |
| Radians | 13π/10 ≈ 4.08407 |
| Gradians | 260 grad |
| Fraction of a turn | 13/20 (65%) |
| Degrees, minutes, seconds | 234° 0′ 0″ |
| Compass bearing | between SW and WSW (closest to southwest (SW)) |
Trigonometric values of 234°
| Function | Value |
|---|---|
| sin 234° | −(√5 + 1)/4 ≈ −0.809017 |
| cos 234° | −√(10 − 2√5)/4 ≈ −0.587785 |
| tan 234° | 1.376382 |
234° on a protractor
How to draw a 234° angle with a protractor
- Subtract from 360°: 360° − 234° = 126°. 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 126°.
- Join the vertex to the dot. The inside angle is 126°; the outside angle, going the long way around, is 234°. Draw the angle arc on the outside and label it 234°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 234° directly.
Drawing it a 234° angle without a protractor (rise and run method)
- 234° = 180° − 54°. Draw a straight line, pick a vertex on it, and build a 54° angle on one side as follows; the angle on the other side of the new line is 126°.
- Draw a straight baseline and measure 7.27 inches (about 7 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 54°, because tan 54° ≈ 1.3764.
- That gives you 126°. The outside (reflex) angle is 234°.
Where you see 234° angles
- The Earth turns 234° on its axis in about 15 h 36 min.
- A 234° 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
234° angle FAQ
What type of angle is 234°?
A 234° angle is a reflex angle, because it is between 180° and 360°.
Does a 234° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 234° is already larger than both. What it does have is an explement (conjugate) of 126°, the angle that completes a full 360° circle.
How many radians is 234 degrees?
234° = 13π/10 radians ≈ 4.0841 rad. To convert degrees to radians, multiply by π/180: 234 × π/180 = 13π/10.
How do I measure a 234° angle on my screen?
Open the online protractor with 234° preset, or type 234 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
