At 154°, this is an obtuse angle, opened up past a square corner but not yet flat. Its supplement is 26°, so a 154° angle and a 26° angle side by side make a straight line.
154° is 77/180 of a full circle, or 77π/90 radians. If you face north and turn 154° clockwise, you end up facing between SE and SSE (closest to south-southeast (SSE)).
154° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 26° |
| Explement (adds to 360°) | 206° |
| Radians | 77π/90 ≈ 2.687807 |
| Gradians | 171.1111 grad |
| Fraction of a turn | 77/180 (42.78%) |
| Degrees, minutes, seconds | 154° 0′ 0″ |
| Compass bearing | between SE and SSE (closest to south-southeast (SSE)) |
Trigonometric values of 154°
| Function | Value |
|---|---|
| sin 154° | 0.438371 |
| cos 154° | −0.898794 |
| tan 154° | −0.487733 |
154° on a protractor
How to draw a 154° 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 154° 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 154°.
Drawing it a 154° angle without a protractor (rise and run method)
- 154° = 180° − 26°. Draw a straight line, pick a vertex on it, and build a 26° angle on one side as follows; the angle on the other side of the new line is 154°.
- 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 4.88 inches (about 4 7/8″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 26°, because tan 26° ≈ 0.4877.
Where you see 154° angles
- The Earth turns 154° on its axis in about 10 h 16 min.
- Obtuse angles like 154° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
154° angle FAQ
What type of angle is 154°?
A 154° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 154°?
The supplement of 154° is 26°, because 154° + 26° = 180°. A 154° angle has no complement, because it is already larger than 90°.
How many radians is 154 degrees?
154° = 77π/90 radians ≈ 2.6878 rad. To convert degrees to radians, multiply by π/180: 154 × π/180 = 77π/90.
How do I measure a 154° angle on my screen?
Open the online protractor with 154° preset, or type 154 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
