257 Degree Angle

A 257° angle is reflex because it measures between 180° and 360°. It is the "outside" of a 103° angle: together they make a full 360° circle.

257° is 257/360 of a full circle, or 257π/180 radians. If you face north and turn 257° clockwise, you end up facing between WSW and W (closest to west-southwest (WSW)).

257° angle facts

Trigonometric values of 257°

257° on a protractor

How to draw a 257° angle with a protractor

1. Subtract from 360°: 360° − 257° = 103°. 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 103°.
4. Join the vertex to the dot. The inside angle is 103°; the outside angle, going the long way around, is 257°. Draw the angle arc on the outside and label it 257°.
5. With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 257° directly.

Drawing it a 257° angle without a protractor (rise and run method)

1. 257° = 180° − 77°. Draw a straight line, pick a vertex on it, and build a 77° angle on one side as follows; the angle on the other side of the new line is 103°.
2. Draw a straight baseline and measure 2.31 inches (about 2 5/16″) 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 77°, because tan 77° ≈ 4.3315.
5. That gives you 103°. The outside (reflex) angle is 257°.

Where you see 257° angles

• The Earth turns 257° on its axis in about 17 h 8 min.
• A 257° 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: 103°
• 30°
• 45°
• 60°
• 90°
• 120°
• 135°
• 180°