A 113° angle is obtuse because it is greater than 90° and less than 180°. Its supplement is 67°, so a 113° angle and a 67° angle side by side make a straight line.
113° is 113/360 of a full circle, or 113π/180 radians. If you face north and turn 113° clockwise, you end up facing between ESE and SE (closest to east-southeast (ESE)).
113° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 67° |
| Explement (adds to 360°) | 247° |
| Radians | 113π/180 ≈ 1.972222 |
| Gradians | 125.5556 grad |
| Fraction of a turn | 113/360 (31.39%) |
| Degrees, minutes, seconds | 113° 0′ 0″ |
| Compass bearing | between ESE and SE (closest to east-southeast (ESE)) |
Trigonometric values of 113°
| Function | Value |
|---|---|
| sin 113° | 0.920505 |
| cos 113° | −0.390731 |
| tan 113° | −2.355852 |
113° on a protractor
How to draw a 113° 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 113° 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 113°.
Drawing it a 113° angle without a protractor (rise and run method)
- 113° = 180° − 67°. Draw a straight line, pick a vertex on it, and build a 67° angle on one side as follows; the angle on the other side of the new line is 113°.
- Draw a straight baseline and measure 4.24 inches (about 4 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 67°, because tan 67° ≈ 2.3559.
Where you see 113° angles
- The Earth turns 113° on its axis in about 7 h 32 min.
- Obtuse angles like 113° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
113° angle FAQ
What type of angle is 113°?
A 113° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 113°?
The supplement of 113° is 67°, because 113° + 67° = 180°. A 113° angle has no complement, because it is already larger than 90°.
How many radians is 113 degrees?
113° = 113π/180 radians ≈ 1.9722 rad. To convert degrees to radians, multiply by π/180: 113 × π/180 = 113π/180.
How do I measure a 113° angle on my screen?
Open the online protractor with 113° preset, or type 113 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
