A 117° angle is an obtuse angle: wider than a right angle (90°) but less than a straight line (180°). Its supplement is 63°, so a 117° angle and a 63° angle side by side make a straight line.
117° is 13/40 of a full circle, or 13π/20 radians. If you face north and turn 117° clockwise, you end up facing between ESE and SE (closest to east-southeast (ESE)).
117° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 63° |
| Explement (adds to 360°) | 243° |
| Radians | 13π/20 ≈ 2.042035 |
| Gradians | 130 grad |
| Fraction of a turn | 13/40 (32.5%) |
| Degrees, minutes, seconds | 117° 0′ 0″ |
| Compass bearing | between ESE and SE (closest to east-southeast (ESE)) |
Trigonometric values of 117°
| Function | Value |
|---|---|
| sin 117° | 0.891007 |
| cos 117° | −0.45399 |
| tan 117° | −1.962611 |
117° on a protractor
How to draw a 117° 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 117° 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 117°.
Drawing it a 117° angle without a protractor (rise and run method)
- 117° = 180° − 63°. Draw a straight line, pick a vertex on it, and build a 63° angle on one side as follows; the angle on the other side of the new line is 117°.
- Draw a straight baseline and measure 5.1 inches (about 5 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 63°, because tan 63° ≈ 1.9626.
Where you see 117° angles
- The Earth turns 117° on its axis in about 7 h 48 min.
- Obtuse angles like 117° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
117° angle FAQ
What type of angle is 117°?
A 117° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 117°?
The supplement of 117° is 63°, because 117° + 63° = 180°. A 117° angle has no complement, because it is already larger than 90°.
How many radians is 117 degrees?
117° = 13π/20 radians ≈ 2.042 rad. To convert degrees to radians, multiply by π/180: 117 × π/180 = 13π/20.
How do I measure a 117° angle on my screen?
Open the online protractor with 117° preset, or type 117 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
