251 Degree Angle

A 251° angle is reflex because it measures between 180° and 360°. It is the "outside" of a 109° angle: together they make a full 360° circle.

251° is 251/360 of a full circle, or 251π/180 radians. If you face north and turn 251° clockwise, you end up facing between WSW and W (closest to west-southwest (WSW)).

251° angle facts

Trigonometric values of 251°

251° on a protractor

How to draw a 251° angle with a protractor

1. Subtract from 360°: 360° − 251° = 109°. 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 109°.
4. Join the vertex to the dot. The inside angle is 109°; the outside angle, going the long way around, is 251°. Draw the angle arc on the outside and label it 251°.
5. With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 251° directly.

Drawing it a 251° angle without a protractor (rise and run method)

1. 251° = 180° − 71°. Draw a straight line, pick a vertex on it, and build a 71° angle on one side as follows; the angle on the other side of the new line is 109°.
2. Draw a straight baseline and measure 3.44 inches (about 3 7/16″) 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 71°, because tan 71° ≈ 2.9042.
5. That gives you 109°. The outside (reflex) angle is 251°.

Where you see 251° angles

• The Earth turns 251° on its axis in about 16 h 44 min.
• A 251° 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: 109°
• 30°
• 45°
• 60°
• 90°
• 120°
• 135°
• 180°