At 157°, this is an obtuse angle, opened up past a square corner but not yet flat. Its supplement is 23°, so a 157° angle and a 23° angle side by side make a straight line.
157° is 157/360 of a full circle, or 157π/180 radians. If you face north and turn 157° clockwise, you end up facing between SE and SSE (closest to south-southeast (SSE)).
157° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 23° |
| Explement (adds to 360°) | 203° |
| Radians | 157π/180 ≈ 2.740167 |
| Gradians | 174.4444 grad |
| Fraction of a turn | 157/360 (43.61%) |
| Degrees, minutes, seconds | 157° 0′ 0″ |
| Compass bearing | between SE and SSE (closest to south-southeast (SSE)) |
Trigonometric values of 157°
| Function | Value |
|---|---|
| sin 157° | 0.390731 |
| cos 157° | −0.920505 |
| tan 157° | −0.424475 |
157° on a protractor
How to draw a 157° 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° 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 157°.
Drawing it a 157° angle without a protractor (rise and run method)
- 157° = 180° − 23°. Draw a straight line, pick a vertex on it, and build a 23° angle on one side as follows; the angle on the other side of the new line is 157°.
- Draw a straight baseline and measure exactly 10 inches along it from the vertex.
- At the 10-inch mark, draw a short line straight up at 90° (use a carpenter's square or the corner of a sheet of paper).
- Measure 4.24 inches (about 4 1/4″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 23°, because tan 23° ≈ 0.4245.
Where you see 157° angles
- The Earth turns 157° on its axis in about 10 h 28 min.
- Obtuse angles like 157° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
157° angle FAQ
What type of angle is 157°?
A 157° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 157°?
The supplement of 157° is 23°, because 157° + 23° = 180°. A 157° angle has no complement, because it is already larger than 90°.
How many radians is 157 degrees?
157° = 157π/180 radians ≈ 2.7402 rad. To convert degrees to radians, multiply by π/180: 157 × π/180 = 157π/180.
How do I measure a 157° angle on my screen?
Open the online protractor with 157° preset, or type 157 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
