At 115°, this is an obtuse angle, opened up past a square corner but not yet flat. Its supplement is 65°, so a 115° angle and a 65° angle side by side make a straight line.
115° is 23/72 of a full circle, or 23π/36 radians. If you face north and turn 115° clockwise, you end up facing between ESE and SE (closest to east-southeast (ESE)).
115° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 65° |
| Explement (adds to 360°) | 245° |
| Radians | 23π/36 ≈ 2.007129 |
| Gradians | 127.7778 grad |
| Fraction of a turn | 23/72 (31.94%) |
| Degrees, minutes, seconds | 115° 0′ 0″ |
| Compass bearing | between ESE and SE (closest to east-southeast (ESE)) |
Trigonometric values of 115°
| Function | Value |
|---|---|
| sin 115° | 0.906308 |
| cos 115° | −0.422618 |
| tan 115° | −2.144507 |
115° on a protractor
How to draw a 115° 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 115° 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 115°.
Drawing it a 115° angle without a protractor (rise and run method)
- 115° = 180° − 65°. Draw a straight line, pick a vertex on it, and build a 65° angle on one side as follows; the angle on the other side of the new line is 115°.
- Draw a straight baseline and measure 4.66 inches (about 4 11/16″) 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 65°, because tan 65° ≈ 2.1445.
Where you see 115° angles
- The Earth turns 115° on its axis in about 7 h 40 min.
- Obtuse angles like 115° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
115° angle FAQ
What type of angle is 115°?
A 115° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 115°?
The supplement of 115° is 65°, because 115° + 65° = 180°. A 115° angle has no complement, because it is already larger than 90°.
How many radians is 115 degrees?
115° = 23π/36 radians ≈ 2.0071 rad. To convert degrees to radians, multiply by π/180: 115 × π/180 = 23π/36.
How do I measure a 115° angle on my screen?
Open the online protractor with 115° preset, or type 115 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
