A 126° angle is an obtuse angle: wider than a right angle (90°) but less than a straight line (180°). Its supplement is 54°, so a 126° angle and a 54° angle side by side make a straight line.
126° is 7/20 of a full circle, or 7π/10 radians. The minute hand of a clock sweeps 126° in 21 minutes. If you face north and turn 126° clockwise, you end up facing between ESE and SE (closest to southeast (SE)).
126° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 54° |
| Explement (adds to 360°) | 234° |
| Radians | 7π/10 ≈ 2.199115 |
| Gradians | 140 grad |
| Fraction of a turn | 7/20 (35%) |
| Degrees, minutes, seconds | 126° 0′ 0″ |
| Compass bearing | between ESE and SE (closest to southeast (SE)) |
Trigonometric values of 126°
| Function | Value |
|---|---|
| sin 126° | (√5 + 1)/4 ≈ 0.809017 |
| cos 126° | −√(10 − 2√5)/4 ≈ −0.587785 |
| tan 126° | −1.376382 |
126° on a protractor
How to draw a 126° angle with a protractor
- Draw a straight line with a ruler. This is the first arm; mark the vertex at one end.
- Place the center mark of the protractor exactly on the vertex and line up the 0° baseline with your line.
- Find 126° on the row of numbers that reads 0° on your line (protractors have two rows running in opposite directions) and make a small dot at the edge.
- Remove the protractor and draw a line from the vertex through the dot. Mark the angle with an arc and label it 126°.
Drawing it a 126° angle without a protractor (rise and run method)
- 126° = 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.
Where you see 126° angles
- The Earth turns 126° on its axis in about 8 h 24 min.
- Obtuse angles like 126° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
126° angle FAQ
What type of angle is 126°?
A 126° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 126°?
The supplement of 126° is 54°, because 126° + 54° = 180°. A 126° angle has no complement, because it is already larger than 90°.
How many radians is 126 degrees?
126° = 7π/10 radians ≈ 2.1991 rad. To convert degrees to radians, multiply by π/180: 126 × π/180 = 7π/10.
How do I measure a 126° angle on my screen?
Open the online protractor with 126° preset, or type 126 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
