359 Degree Angle

A 359° angle is reflex because it measures between 180° and 360°. It is the "outside" of a 1° angle: together they make a full 360° circle.

359° is 359/360 of a full circle, or 359π/180 radians. If you face north and turn 359° clockwise, you end up facing between NNW and N (closest to north (N)).

359° angle facts

Trigonometric values of 359°

359° on a protractor

How to draw a 359° angle with a protractor

1. Subtract from 360°: 360° − 359° = 1°. A standard protractor only goes to 180°, so you draw the smaller angle first.
2. Draw a straight line with a ruler and mark the vertex at one end.
3. Place the protractor's center mark on the vertex, line up the 0° baseline with your line, and make a dot at 1°.
4. Join the vertex to the dot. The inside angle is 1°; the outside angle, going the long way around, is 359°. Draw the angle arc on the outside and label it 359°.
5. With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 359° directly.

Drawing it a 359° angle without a protractor (rise and run method)

1. Draw a straight baseline and measure exactly 10 inches along it from the vertex.
2. At the 10-inch mark, draw a short line straight up at 90° (use a carpenter's square or the corner of a sheet of paper).
3. Measure 0.17 inches (about 3/16″) up that line and make a mark.
4. Join the mark to the vertex. The angle at the vertex is 1°, because tan 1° ≈ 0.0175.
5. That gives you 1°. The outside (reflex) angle is 359°.

Where you see 359° angles

• The Earth turns 359° on its axis in about 23 h 56 min.
• A 359° 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

• Explement: 1°
• 30°
• 45°
• 60°
• 90°
• 120°
• 135°
• 180°