A 158° angle is obtuse because it is greater than 90° and less than 180°. Its supplement is 22°, so a 158° angle and a 22° angle side by side make a straight line.
158° is 79/180 of a full circle, or 79π/90 radians. If you face north and turn 158° clockwise, you end up facing between SSE and S (closest to south-southeast (SSE)).
158° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 22° |
| Explement (adds to 360°) | 202° |
| Radians | 79π/90 ≈ 2.75762 |
| Gradians | 175.5556 grad |
| Fraction of a turn | 79/180 (43.89%) |
| Degrees, minutes, seconds | 158° 0′ 0″ |
| Compass bearing | between SSE and S (closest to south-southeast (SSE)) |
Trigonometric values of 158°
| Function | Value |
|---|---|
| sin 158° | 0.374607 |
| cos 158° | −0.927184 |
| tan 158° | −0.404026 |
158° on a protractor
How to draw a 158° 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 158° 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 158°.
Drawing it a 158° angle without a protractor (rise and run method)
- 158° = 180° − 22°. Draw a straight line, pick a vertex on it, and build a 22° angle on one side as follows; the angle on the other side of the new line is 158°.
- 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 4.04 inches (about 4 1/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 22°, because tan 22° ≈ 0.404.
Where you see 158° angles
- The Earth turns 158° on its axis in about 10 h 32 min.
- Obtuse angles like 158° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
158° angle FAQ
What type of angle is 158°?
A 158° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 158°?
The supplement of 158° is 22°, because 158° + 22° = 180°. A 158° angle has no complement, because it is already larger than 90°.
How many radians is 158 degrees?
158° = 79π/90 radians ≈ 2.7576 rad. To convert degrees to radians, multiply by π/180: 158 × π/180 = 79π/90.
How do I measure a 158° angle on my screen?
Open the online protractor with 158° preset, or type 158 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
