At 103°, this is an obtuse angle, opened up past a square corner but not yet flat. Its supplement is 77°, so a 103° angle and a 77° angle side by side make a straight line.
103° is 103/360 of a full circle, or 103π/180 radians. If you face north and turn 103° clockwise, you end up facing between E and ESE (closest to east-southeast (ESE)).
103° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 77° |
| Explement (adds to 360°) | 257° |
| Radians | 103π/180 ≈ 1.797689 |
| Gradians | 114.4444 grad |
| Fraction of a turn | 103/360 (28.61%) |
| Degrees, minutes, seconds | 103° 0′ 0″ |
| Compass bearing | between E and ESE (closest to east-southeast (ESE)) |
Trigonometric values of 103°
| Function | Value |
|---|---|
| sin 103° | 0.97437 |
| cos 103° | −0.224951 |
| tan 103° | −4.331476 |
103° on a protractor
How to draw a 103° 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 103° 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 103°.
Drawing it a 103° angle without a protractor (rise and run method)
- 103° = 180° − 77°. Draw a straight line, pick a vertex on it, and build a 77° angle on one side as follows; the angle on the other side of the new line is 103°.
- Draw a straight baseline and measure 2.31 inches (about 2 5/16″) 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 77°, because tan 77° ≈ 4.3315.
Where you see 103° angles
- The Earth turns 103° on its axis in about 6 h 52 min.
- Obtuse angles like 103° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
103° angle FAQ
What type of angle is 103°?
A 103° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 103°?
The supplement of 103° is 77°, because 103° + 77° = 180°. A 103° angle has no complement, because it is already larger than 90°.
How many radians is 103 degrees?
103° = 103π/180 radians ≈ 1.7977 rad. To convert degrees to radians, multiply by π/180: 103 × π/180 = 103π/180.
How do I measure a 103° angle on my screen?
Open the online protractor with 103° preset, or type 103 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
