At 112.5°, this is an obtuse angle, opened up past a square corner but not yet flat. Its supplement is 67.5°, so a 112.5° angle and a 67.5° angle side by side make a straight line.
112.5° is 5/16 of a full circle, or 5π/8 radians. If you face north and turn 112.5° clockwise, you end up facing due east-southeast (ESE).
112.5° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 67.5° |
| Explement (adds to 360°) | 247.5° |
| Radians | 5π/8 ≈ 1.963495 |
| Gradians | 125 grad |
| Fraction of a turn | 5/16 (31.25%) |
| Degrees, minutes, seconds | 112° 30′ 0″ |
| Compass bearing | east-southeast (ESE) |
Trigonometric values of 112.5°
| Function | Value |
|---|---|
| sin 112.5° | √(2 + √2)/2 ≈ 0.92388 |
| cos 112.5° | −√(2 − √2)/2 ≈ −0.382683 |
| tan 112.5° | −(√2 + 1) ≈ −2.414214 |
112.5° on a protractor
How to draw a 112.5° 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 112.5° 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. 112.5° falls between the 112° and 113° marks; estimate the position carefully.
- Remove the protractor and draw a line from the vertex through the dot. Mark the angle with an arc and label it 112.5°.
Drawing it a 112.5° angle without a protractor (compass and ruler)
- Draw a 90° angle: construct a perpendicular line (draw arcs from two points on the line and join their crossing points).
- Using the second arm as your new base, add a 22.5° angle on the outside: construct a 45° angle, then bisect it.
- The angle between the first arm and the new arm is 90° + 22.5° = 112.5°.
Where you see 112.5° angles
- The Earth turns 112.5° on its axis in about 7 h 30 min.
- Obtuse angles like 112.5° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
112.5° angle FAQ
What type of angle is 112.5°?
A 112.5° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 112.5°?
The supplement of 112.5° is 67.5°, because 112.5° + 67.5° = 180°. A 112.5° angle has no complement, because it is already larger than 90°.
How many radians is 112.5 degrees?
112.5° = 5π/8 radians ≈ 1.9635 rad. To convert degrees to radians, multiply by π/180: 112.5 × π/180 = 5π/8.
How do I measure a 112.5° angle on my screen?
Open the online protractor with 112.5° preset, or type 112.5 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
