A 162° angle is an obtuse angle: wider than a right angle (90°) but less than a straight line (180°). Its supplement is 18°, so a 162° angle and an 18° angle side by side make a straight line.
162° is 9/20 of a full circle, or 9π/10 radians. The minute hand of a clock sweeps 162° in 27 minutes. If you face north and turn 162° clockwise, you end up facing between SSE and S (closest to south-southeast (SSE)).
162° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 18° |
| Explement (adds to 360°) | 198° |
| Radians | 9π/10 ≈ 2.827433 |
| Gradians | 180 grad |
| Fraction of a turn | 9/20 (45%) |
| Degrees, minutes, seconds | 162° 0′ 0″ |
| Compass bearing | between SSE and S (closest to south-southeast (SSE)) |
Trigonometric values of 162°
| Function | Value |
|---|---|
| sin 162° | (√5 − 1)/4 ≈ 0.309017 |
| cos 162° | −√(10 + 2√5)/4 ≈ −0.951057 |
| tan 162° | −0.32492 |
162° on a protractor
How to draw a 162° 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 162° 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 162°.
Drawing it a 162° angle without a protractor (rise and run method)
- 162° = 180° − 18°. Draw a straight line, pick a vertex on it, and build an 18° angle on one side as follows; the angle on the other side of the new line is 162°.
- 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 3.25 inches (about 3 1/4″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 18°, because tan 18° ≈ 0.3249.
Where you see 162° angles
- Each interior corner of a regular 20-sided polygon measures 162°.
- The Earth turns 162° on its axis in about 10 h 48 min.
- Obtuse angles like 162° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
162° angle FAQ
What type of angle is 162°?
A 162° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 162°?
The supplement of 162° is 18°, because 162° + 18° = 180°. A 162° angle has no complement, because it is already larger than 90°.
How many radians is 162 degrees?
162° = 9π/10 radians ≈ 2.8274 rad. To convert degrees to radians, multiply by π/180: 162 × π/180 = 9π/10.
How do I measure a 162° angle on my screen?
Open the online protractor with 162° preset, or type 162 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
