266 Degree Angle

A 266° angle is reflex because it measures between 180° and 360°. It is the "outside" of a 94° angle: together they make a full 360° circle.

266° is 133/180 of a full circle, or 133π/90 radians. If you face north and turn 266° clockwise, you end up facing between WSW and W (closest to west (W)).

266° angle facts

Trigonometric values of 266°

266° on a protractor

How to draw a 266° angle with a protractor

1. Subtract from 360°: 360° − 266° = 94°. 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 94°.
4. Join the vertex to the dot. The inside angle is 94°; the outside angle, going the long way around, is 266°. Draw the angle arc on the outside and label it 266°.
5. With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 266° directly.

Drawing it a 266° angle without a protractor (rise and run method)

1. 266° = 180° − 86°. Draw a straight line, pick a vertex on it, and build an 86° angle on one side as follows; the angle on the other side of the new line is 94°.
2. Draw a straight baseline and measure 0.7 inches (about 11/16″) along it from the vertex.
3. At that mark, draw a line straight up at 90° and measure exactly 10 inches up it.
4. Join the top mark to the vertex. The angle at the vertex is 86°, because tan 86° ≈ 14.3007.
5. That gives you 94°. The outside (reflex) angle is 266°.

Where you see 266° angles

• The Earth turns 266° on its axis in about 17 h 44 min.
• A 266° 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: 94°
• Half: 133°
• 30°
• 45°
• 60°
• 90°
• 120°
• 135°
• 180°