A 96° angle is an obtuse angle: wider than a right angle (90°) but less than a straight line (180°). Its supplement is 84°, so a 96° angle and an 84° angle side by side make a straight line.
96° is 4/15 of a full circle, or 8π/15 radians. The minute hand of a clock sweeps 96° in 16 minutes. If you face north and turn 96° clockwise, you end up facing between E and ESE (closest to east (E)).
96° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 84° |
| Explement (adds to 360°) | 264° |
| Radians | 8π/15 ≈ 1.675516 |
| Gradians | 106.6667 grad |
| Fraction of a turn | 4/15 (26.67%) |
| Degrees, minutes, seconds | 96° 0′ 0″ |
| Compass bearing | between E and ESE (closest to east (E)) |
Trigonometric values of 96°
| Function | Value |
|---|---|
| sin 96° | 0.994522 |
| cos 96° | −0.104528 |
| tan 96° | −9.514364 |
96° on a protractor
How to draw a 96° 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 96° 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 96°.
Drawing it a 96° angle without a protractor (rise and run method)
- 96° = 180° − 84°. Draw a straight line, pick a vertex on it, and build an 84° angle on one side as follows; the angle on the other side of the new line is 96°.
- Draw a straight baseline and measure 1.05 inches (about 1 1/16″) along it from the vertex.
- At that mark, draw a line straight up at 90° and measure exactly 10 inches up it.
- Join the top mark to the vertex. The angle at the vertex is 84°, because tan 84° ≈ 9.5144.
Where you see 96° angles
- The Earth turns 96° on its axis in about 6 h 24 min.
- Obtuse angles like 96° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
96° angle FAQ
What type of angle is 96°?
A 96° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 96°?
The supplement of 96° is 84°, because 96° + 84° = 180°. A 96° angle has no complement, because it is already larger than 90°.
How many radians is 96 degrees?
96° = 8π/15 radians ≈ 1.6755 rad. To convert degrees to radians, multiply by π/180: 96 × π/180 = 8π/15.
How do I measure a 96° angle on my screen?
Open the online protractor with 96° preset, or type 96 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
