A 72° angle is an acute angle: it is smaller than a right angle (90°). It is more than half of a right angle. Add 18° more and you get a square corner.
72° is one fifth (1/5) of a full circle, or 2π/5 radians. The minute hand of a clock sweeps 72° in 12 minutes. If you face north and turn 72° clockwise, you end up facing between ENE and E (closest to east-northeast (ENE)).
72° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 18° |
| Supplement (adds to 180°) | 108° |
| Explement (adds to 360°) | 288° |
| Radians | 2π/5 ≈ 1.256637 |
| Gradians | 80 grad |
| Fraction of a turn | one fifth (1/5) (20%) |
| Degrees, minutes, seconds | 72° 0′ 0″ |
| Slope (grade) | 307.77% |
| Roof pitch | 36.93/12 |
| Compass bearing | between ENE and E (closest to east-northeast (ENE)) |
Trigonometric values of 72°
| Function | Value |
|---|---|
| sin 72° | √(10 + 2√5)/4 ≈ 0.951057 |
| cos 72° | (√5 − 1)/4 ≈ 0.309017 |
| tan 72° | 3.077684 |
72° on a protractor
How to draw a 72° 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 72° 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 72°.
Drawing it a 72° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 3.25 inches (about 3 1/4″) 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 72°, because tan 72° ≈ 3.0777.
Where you see 72° angles
- Five equally spaced fan blades or spokes are 72° apart.
- 72° of latitude on Earth spans roughly 4,972 miles north to south.
- The Earth turns 72° on its axis in about 4 h 48 min.
- Narrow acute angles like 72° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
72° angle FAQ
What type of angle is 72°?
A 72° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 72°?
The complement of 72° is 18° (together they make 90°), and the supplement is 108° (together they make 180°).
How many radians is 72 degrees?
72° = 2π/5 radians ≈ 1.2566 rad. To convert degrees to radians, multiply by π/180: 72 × π/180 = 2π/5.
How do I measure a 72° angle on my screen?
Open the online protractor with 72° preset, or type 72 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
