218 Degree Angle

A 218° angle is reflex because it measures between 180° and 360°. It is the "outside" of a 142° angle: together they make a full 360° circle.

218° is 109/180 of a full circle, or 109π/90 radians. If you face north and turn 218° clockwise, you end up facing between SSW and SW (closest to southwest (SW)).

218° angle facts

Trigonometric values of 218°

218° on a protractor

How to draw a 218° angle with a protractor

1. Subtract from 360°: 360° − 218° = 142°. 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 142°.
4. Join the vertex to the dot. The inside angle is 142°; the outside angle, going the long way around, is 218°. Draw the angle arc on the outside and label it 218°.
5. With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 218° directly.

Drawing it a 218° angle without a protractor (rise and run method)

1. 218° = 180° − 38°. Draw a straight line, pick a vertex on it, and build a 38° angle on one side as follows; the angle on the other side of the new line is 142°.
2. Draw a straight baseline and measure exactly 10 inches along it from the vertex.
3. 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).
4. Measure 7.81 inches (about 7 13/16″) up that line and make a mark.
5. Join the mark to the vertex. The angle at the vertex is 38°, because tan 38° ≈ 0.7813.
6. That gives you 142°. The outside (reflex) angle is 218°.

Where you see 218° angles

• The Earth turns 218° on its axis in about 14 h 32 min.
• A 218° 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: 142°
• Half: 109°
• 30°
• 45°
• 60°
• 90°
• 120°
• 135°
• 180°