239 Degree Angle

A 239° angle is reflex because it measures between 180° and 360°. It is the "outside" of a 121° angle: together they make a full 360° circle.

239° is 239/360 of a full circle, or 239π/180 radians. If you face north and turn 239° clockwise, you end up facing between SW and WSW (closest to west-southwest (WSW)).

239° angle facts

Trigonometric values of 239°

239° on a protractor

How to draw a 239° angle with a protractor

1. Subtract from 360°: 360° − 239° = 121°. 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 121°.
4. Join the vertex to the dot. The inside angle is 121°; the outside angle, going the long way around, is 239°. Draw the angle arc on the outside and label it 239°.
5. With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 239° directly.

Drawing it a 239° angle without a protractor (rise and run method)

1. 239° = 180° − 59°. Draw a straight line, pick a vertex on it, and build a 59° angle on one side as follows; the angle on the other side of the new line is 121°.
2. Draw a straight baseline and measure 6.01 inches (about 6″) 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 59°, because tan 59° ≈ 1.6643.
5. That gives you 121°. The outside (reflex) angle is 239°.

Where you see 239° angles

• The Earth turns 239° on its axis in about 15 h 56 min.
• A 239° 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: 121°
• 30°
• 45°
• 60°
• 90°
• 120°
• 135°
• 180°