269 Degree Angle

A 269° angle is reflex because it measures between 180° and 360°. It is the "outside" of a 91° angle: together they make a full 360° circle.

269° is 269/360 of a full circle, or 269π/180 radians. If you face north and turn 269° clockwise, you end up facing between WSW and W (closest to west (W)).

269° angle facts

Trigonometric values of 269°

269° on a protractor

How to draw a 269° angle with a protractor

1. Subtract from 360°: 360° − 269° = 91°. 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 91°.
4. Join the vertex to the dot. The inside angle is 91°; the outside angle, going the long way around, is 269°. Draw the angle arc on the outside and label it 269°.
5. With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 269° directly.

Drawing it a 269° angle without a protractor (rise and run method)

1. 269° = 180° − 89°. Draw a straight line, pick a vertex on it, and build an 89° angle on one side as follows; the angle on the other side of the new line is 91°.
2. Draw a straight baseline and measure 0.17 inches (about 3/16″) 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 89°, because tan 89° ≈ 57.29.
5. That gives you 91°. The outside (reflex) angle is 269°.

Where you see 269° angles

• The Earth turns 269° on its axis in about 17 h 56 min.
• A 269° 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: 91°
• 30°
• 45°
• 60°
• 90°
• 120°
• 135°
• 180°