An 80° angle is classed as acute because it measures less than 90°. It is more than half of a right angle. Add 10° more and you get a square corner.
80° is 2/9 of a full circle, or 4π/9 radians. If you face north and turn 80° clockwise, you end up facing between ENE and E (closest to east (E)).
80° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 10° |
| Supplement (adds to 180°) | 100° |
| Explement (adds to 360°) | 280° |
| Radians | 4π/9 ≈ 1.396263 |
| Gradians | 88.8889 grad |
| Fraction of a turn | 2/9 (22.22%) |
| Degrees, minutes, seconds | 80° 0′ 0″ |
| Slope (grade) | 567.13% |
| Roof pitch | 68.06/12 |
| Compass bearing | between ENE and E (closest to east (E)) |
Trigonometric values of 80°
| Function | Value |
|---|---|
| sin 80° | 0.984808 |
| cos 80° | 0.173648 |
| tan 80° | 5.671282 |
80° on a protractor
How to draw an 80° 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 80° 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 80°.
Drawing it an 80° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 1.76 inches (about 1 3/4″) 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 80°, because tan 80° ≈ 5.6713.
Where you see 80° angles
- 80° of latitude on Earth spans roughly 5,524 miles north to south.
- The Earth turns 80° on its axis in about 5 h 20 min.
- Narrow acute angles like 80° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
80° angle FAQ
What type of angle is 80°?
An 80° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 80°?
The complement of 80° is 10° (together they make 90°), and the supplement is 100° (together they make 180°).
How many radians is 80 degrees?
80° = 4π/9 radians ≈ 1.3963 rad. To convert degrees to radians, multiply by π/180: 80 × π/180 = 4π/9.
How do I measure an 80° angle on my screen?
Open the online protractor with 80° preset, or type 80 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
