At 109°, this is an obtuse angle, opened up past a square corner but not yet flat. Its supplement is 71°, so a 109° angle and a 71° angle side by side make a straight line.
109° is 109/360 of a full circle, or 109π/180 radians. If you face north and turn 109° clockwise, you end up facing between E and ESE (closest to east-southeast (ESE)).
109° angle facts
| Angle type | Obtuse angle (between 90° and 180°) |
|---|---|
| Supplement (adds to 180°) | 71° |
| Explement (adds to 360°) | 251° |
| Radians | 109π/180 ≈ 1.902409 |
| Gradians | 121.1111 grad |
| Fraction of a turn | 109/360 (30.28%) |
| Degrees, minutes, seconds | 109° 0′ 0″ |
| Compass bearing | between E and ESE (closest to east-southeast (ESE)) |
Trigonometric values of 109°
| Function | Value |
|---|---|
| sin 109° | 0.945519 |
| cos 109° | −0.325568 |
| tan 109° | −2.904211 |
109° on a protractor
How to draw a 109° 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 109° 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 109°.
Drawing it a 109° angle without a protractor (rise and run method)
- 109° = 180° − 71°. Draw a straight line, pick a vertex on it, and build a 71° angle on one side as follows; the angle on the other side of the new line is 109°.
- Draw a straight baseline and measure 3.44 inches (about 3 7/16″) 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 71°, because tan 71° ≈ 2.9042.
Where you see 109° angles
- The tetrahedral bond angle in methane (CH₄) is about 109.5°.
- The Earth turns 109° on its axis in about 7 h 16 min.
- Obtuse angles like 109° appear in reclining chair backs, open laptop screens, fan blades, and the corners of many-sided polygons.
Related angles
109° angle FAQ
What type of angle is 109°?
A 109° angle is an obtuse angle, because it is between 90° and 180°.
What is the supplement of 109°?
The supplement of 109° is 71°, because 109° + 71° = 180°. A 109° angle has no complement, because it is already larger than 90°.
How many radians is 109 degrees?
109° = 109π/180 radians ≈ 1.9024 rad. To convert degrees to radians, multiply by π/180: 109 × π/180 = 109π/180.
How do I measure a 109° angle on my screen?
Open the online protractor with 109° preset, or type 109 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
