A 150° angle is an obtuse angle: wider than a right angle (90°) but less than a straight line (180°). Its supplement is 30°, so a 150° angle and a 30° angle side by side make a straight line.
150° is 5/12 of a full circle, or 5π/6 radians. The minute hand of a clock sweeps 150° in 25 minutes. If you face north and turn 150° clockwise, you end up facing between SE and SSE (closest to south-southeast (SSE)).
150° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 30° |
| Explement (adds to 360°) | 210° |
| Radians | 5π/6 ≈ 2.617994 |
| Gradians | 166.6667 grad |
| Fraction of a turn | 5/12 (41.67%) |
| Degrees, minutes, seconds | 150° 0′ 0″ |
| Compass bearing | between SE and SSE (closest to south-southeast (SSE)) |
Trigonometric values of 150°
| Function | Value |
|---|---|
| sin 150° | 1/2 ≈ 0.5 |
| cos 150° | −√3/2 ≈ −0.866025 |
| tan 150° | −√3/3 ≈ −0.57735 |
150° on a protractor
How to draw a 150° 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 150° 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 150°.
Drawing it a 150° angle without a protractor (compass and ruler)
- Draw a 180° angle: draw a straight line.
- Inside it, starting from the second arm, mark a 30° angle: construct a 60° angle, then bisect it.
- What is left between the first arm and the new line is 180° − 30° = 150°.
Where you see 150° angles
- At 5:00 the hands of a clock form a 150° angle.
- Each interior corner of a regular dodecagon measures 150°.
- The Earth turns 150° on its axis in about 10 hours.
- Obtuse angles like 150° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
150° angle FAQ
What type of angle is 150°?
A 150° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 150°?
The supplement of 150° is 30°, because 150° + 30° = 180°. A 150° angle has no complement, because it is already larger than 90°.
How many radians is 150 degrees?
150° = 5π/6 radians ≈ 2.618 rad. To convert degrees to radians, multiply by π/180: 150 × π/180 = 5π/6.
How do I measure a 150° angle on my screen?
Open the online protractor with 150° preset, or type 150 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
