A 114° angle is an obtuse angle: wider than a right angle (90°) but less than a straight line (180°). Its supplement is 66°, so a 114° angle and a 66° angle side by side make a straight line.
114° is 19/60 of a full circle, or 19π/30 radians. The minute hand of a clock sweeps 114° in 19 minutes. If you face north and turn 114° clockwise, you end up facing between ESE and SE (closest to east-southeast (ESE)).
114° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 66° |
| Explement (adds to 360°) | 246° |
| Radians | 19π/30 ≈ 1.989675 |
| Gradians | 126.6667 grad |
| Fraction of a turn | 19/60 (31.67%) |
| Degrees, minutes, seconds | 114° 0′ 0″ |
| Compass bearing | between ESE and SE (closest to east-southeast (ESE)) |
Trigonometric values of 114°
| Function | Value |
|---|---|
| sin 114° | 0.913545 |
| cos 114° | −0.406737 |
| tan 114° | −2.246037 |
114° on a protractor
How to draw a 114° 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 114° 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 114°.
Drawing it a 114° angle without a protractor (rise and run method)
- 114° = 180° − 66°. Draw a straight line, pick a vertex on it, and build a 66° angle on one side as follows; the angle on the other side of the new line is 114°.
- Draw a straight baseline and measure 4.45 inches (about 4 7/16″) 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 66°, because tan 66° ≈ 2.246.
Where you see 114° angles
- The Earth turns 114° on its axis in about 7 h 36 min.
- Obtuse angles like 114° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
114° angle FAQ
What type of angle is 114°?
A 114° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 114°?
The supplement of 114° is 66°, because 114° + 66° = 180°. A 114° angle has no complement, because it is already larger than 90°.
How many radians is 114 degrees?
114° = 19π/30 radians ≈ 1.9897 rad. To convert degrees to radians, multiply by π/180: 114 × π/180 = 19π/30.
How do I measure a 114° angle on my screen?
Open the online protractor with 114° preset, or type 114 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
