188 Degree Angle

A 188° angle is reflex because it measures between 180° and 360°. It is the "outside" of a 172° angle: together they make a full 360° circle.

188° is 47/90 of a full circle, or 47π/45 radians. If you face north and turn 188° clockwise, you end up facing between S and SSW (closest to south (S)).

188° angle facts

Trigonometric values of 188°

188° on a protractor

How to draw a 188° angle with a protractor

1. Subtract from 360°: 360° − 188° = 172°. 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 172°.
4. Join the vertex to the dot. The inside angle is 172°; the outside angle, going the long way around, is 188°. Draw the angle arc on the outside and label it 188°.
5. With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 188° directly.

Drawing it a 188° angle without a protractor (rise and run method)

1. 188° = 180° − 8°. Draw a straight line, pick a vertex on it, and build an 8° angle on one side as follows; the angle on the other side of the new line is 172°.
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 1.41 inches (about 1 3/8″) up that line and make a mark.
5. Join the mark to the vertex. The angle at the vertex is 8°, because tan 8° ≈ 0.1405.
6. That gives you 172°. The outside (reflex) angle is 188°.

Where you see 188° angles

• The Earth turns 188° on its axis in about 12 h 32 min.
• A 188° 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: 172°
• Half: 94°
• 30°
• 45°
• 60°
• 90°
• 120°
• 135°
• 180°