At 157.5°, this is an obtuse angle, opened up past a square corner but not yet flat. Its supplement is 22.5°, so a 157.5° angle and a 22.5° angle side by side make a straight line.
157.5° is 7/16 of a full circle, or 7π/8 radians. If you face north and turn 157.5° clockwise, you end up facing due south-southeast (SSE).
157.5° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 22.5° |
| Explement (adds to 360°) | 202.5° |
| Radians | 7π/8 ≈ 2.748894 |
| Gradians | 175 grad |
| Fraction of a turn | 7/16 (43.75%) |
| Degrees, minutes, seconds | 157° 30′ 0″ |
| Compass bearing | south-southeast (SSE) |
Trigonometric values of 157.5°
| Function | Value |
|---|---|
| sin 157.5° | √(2 − √2)/2 ≈ 0.382683 |
| cos 157.5° | −√(2 + √2)/2 ≈ −0.92388 |
| tan 157.5° | −(√2 − 1) ≈ −0.414214 |
157.5° on a protractor
How to draw a 157.5° 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 157.5° 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. 157.5° falls between the 157° and 158° 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 157.5°.
Drawing it a 157.5° angle without a protractor (compass and ruler)
- Draw a 180° angle: draw a straight line.
- Inside it, starting from the second arm, mark a 22.5° angle: construct a 45° angle, then bisect it.
- What is left between the first arm and the new line is 180° − 22.5° = 157.5°.
Where you see 157.5° angles
- Each interior corner of a regular 16-sided polygon measures 157.5°.
- The Earth turns 157.5° on its axis in about 10 h 30 min.
- Obtuse angles like 157.5° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
157.5° angle FAQ
What type of angle is 157.5°?
A 157.5° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 157.5°?
The supplement of 157.5° is 22.5°, because 157.5° + 22.5° = 180°. A 157.5° angle has no complement, because it is already larger than 90°.
How many radians is 157.5 degrees?
157.5° = 7π/8 radians ≈ 2.7489 rad. To convert degrees to radians, multiply by π/180: 157.5 × π/180 = 7π/8.
How do I measure a 157.5° angle on my screen?
Open the online protractor with 157.5° preset, or type 157.5 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
