A 65° angle is classed as acute because it measures less than 90°. It is more than half of a right angle. Add 25° more and you get a square corner.
65° is 13/72 of a full circle, or 13π/36 radians. If you face north and turn 65° clockwise, you end up facing between NE and ENE (closest to east-northeast (ENE)).
65° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 25° |
| Supplement (adds to 180°) | 115° |
| Explement (adds to 360°) | 295° |
| Radians | 13π/36 ≈ 1.134464 |
| Gradians | 72.2222 grad |
| Fraction of a turn | 13/72 (18.06%) |
| Degrees, minutes, seconds | 65° 0′ 0″ |
| Slope (grade) | 214.45% |
| Roof pitch | 25.73/12 |
| Compass bearing | between NE and ENE (closest to east-northeast (ENE)) |
Trigonometric values of 65°
| Function | Value |
|---|---|
| sin 65° | 0.906308 |
| cos 65° | 0.422618 |
| tan 65° | 2.144507 |
65° on a protractor
How to draw a 65° 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 65° 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 65°.
Drawing it a 65° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 4.66 inches (about 4 11/16″) 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 65°, because tan 65° ≈ 2.1445.
Where you see 65° angles
- 65° of latitude on Earth spans roughly 4,488 miles north to south.
- The Earth turns 65° on its axis in about 4 h 20 min.
- Narrow acute angles like 65° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
65° angle FAQ
What type of angle is 65°?
A 65° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 65°?
The complement of 65° is 25° (together they make 90°), and the supplement is 115° (together they make 180°).
How many radians is 65 degrees?
65° = 13π/36 radians ≈ 1.1345 rad. To convert degrees to radians, multiply by π/180: 65 × π/180 = 13π/36.
What is 65° as a slope or roof pitch?
65° is a 214.5% slope, which is a roof pitch of 25.73/12 (a rise of about 25 3/4 inches for every 12 inches of run).
