A 102° angle is an obtuse angle: wider than a right angle (90°) but less than a straight line (180°). Its supplement is 78°, so a 102° angle and a 78° angle side by side make a straight line.
102° is 17/60 of a full circle, or 17π/30 radians. The minute hand of a clock sweeps 102° in 17 minutes. If you face north and turn 102° clockwise, you end up facing between E and ESE (closest to east-southeast (ESE)).
102° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 78° |
| Explement (adds to 360°) | 258° |
| Radians | 17π/30 ≈ 1.780236 |
| Gradians | 113.3333 grad |
| Fraction of a turn | 17/60 (28.33%) |
| Degrees, minutes, seconds | 102° 0′ 0″ |
| Compass bearing | between E and ESE (closest to east-southeast (ESE)) |
Trigonometric values of 102°
| Function | Value |
|---|---|
| sin 102° | 0.978148 |
| cos 102° | −0.207912 |
| tan 102° | −4.70463 |
102° on a protractor
How to draw a 102° 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 102° 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 102°.
Drawing it a 102° angle without a protractor (rise and run method)
- 102° = 180° − 78°. Draw a straight line, pick a vertex on it, and build a 78° angle on one side as follows; the angle on the other side of the new line is 102°.
- Draw a straight baseline and measure 2.13 inches (about 2 1/8″) 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 78°, because tan 78° ≈ 4.7046.
Where you see 102° angles
- The Earth turns 102° on its axis in about 6 h 48 min.
- Obtuse angles like 102° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
102° angle FAQ
What type of angle is 102°?
A 102° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 102°?
The supplement of 102° is 78°, because 102° + 78° = 180°. A 102° angle has no complement, because it is already larger than 90°.
How many radians is 102 degrees?
102° = 17π/30 radians ≈ 1.7802 rad. To convert degrees to radians, multiply by π/180: 102 × π/180 = 17π/30.
How do I measure a 102° angle on my screen?
Open the online protractor with 102° preset, or type 102 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
