A 302° angle is reflex because it measures between 180° and 360°. It is the "outside" of a 58° angle: together they make a full 360° circle.
302° is 151/180 of a full circle, or 151π/90 radians. If you face north and turn 302° clockwise, you end up facing between WNW and NW (closest to west-northwest (WNW)).
302° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 58° |
| Radians | 151π/90 ≈ 5.270894 |
| Gradians | 335.5556 grad |
| Fraction of a turn | 151/180 (83.89%) |
| Degrees, minutes, seconds | 302° 0′ 0″ |
| Compass bearing | between WNW and NW (closest to west-northwest (WNW)) |
Trigonometric values of 302°
| Function | Value |
|---|---|
| sin 302° | −0.848048 |
| cos 302° | 0.529919 |
| tan 302° | −1.600335 |
302° on a protractor
How to draw a 302° angle with a protractor
- Subtract from 360°: 360° − 302° = 58°. A standard protractor only goes to 180°, so you draw the smaller angle first.
- Draw a straight line with a ruler and mark the vertex at one end.
- Place the protractor's center mark on the vertex, line up the 0° baseline with your line, and make a dot at 58°.
- Join the vertex to the dot. The inside angle is 58°; the outside angle, going the long way around, is 302°. Draw the angle arc on the outside and label it 302°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 302° directly.
Drawing it a 302° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 6.25 inches (about 6 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 58°, because tan 58° ≈ 1.6003.
- That gives you 58°. The outside (reflex) angle is 302°.
Where you see 302° angles
- The Earth turns 302° on its axis in about 20 h 8 min.
- A 302° reflex angle is what you measure when you go the "long way" around, like the outside corner of a building or a turn of more than half a circle.
Related angles
302° angle FAQ
What type of angle is 302°?
A 302° angle is a reflex angle, because it is between 180° and 360°.
Does a 302° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 302° is already larger than both. What it does have is an explement (conjugate) of 58°, the angle that completes a full 360° circle.
How many radians is 302 degrees?
302° = 151π/90 radians ≈ 5.2709 rad. To convert degrees to radians, multiply by π/180: 302 × π/180 = 151π/90.
How do I measure a 302° angle on my screen?
Open the online protractor with 302° preset, or type 302 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
