221 Degree Angle

A 221° angle is reflex because it measures between 180° and 360°. It is the "outside" of a 139° angle: together they make a full 360° circle.

221° is 221/360 of a full circle, or 221π/180 radians. If you face north and turn 221° clockwise, you end up facing between SSW and SW (closest to southwest (SW)).

221° angle facts

Trigonometric values of 221°

221° on a protractor

How to draw a 221° angle with a protractor

1. Subtract from 360°: 360° − 221° = 139°. 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 139°.
4. Join the vertex to the dot. The inside angle is 139°; the outside angle, going the long way around, is 221°. Draw the angle arc on the outside and label it 221°.
5. With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 221° directly.

Drawing it a 221° angle without a protractor (rise and run method)

1. 221° = 180° − 41°. Draw a straight line, pick a vertex on it, and build a 41° angle on one side as follows; the angle on the other side of the new line is 139°.
2. Draw a straight baseline and measure exactly 10 inches along it from the vertex.
3. At the 10-inch mark, draw a short line straight up at 90° (use a carpenter's square or the corner of a sheet of paper).
4. Measure 8.69 inches (about 8 11/16″) up that line and make a mark.
5. Join the mark to the vertex. The angle at the vertex is 41°, because tan 41° ≈ 0.8693.
6. That gives you 139°. The outside (reflex) angle is 221°.

Where you see 221° angles

• The Earth turns 221° on its axis in about 14 h 44 min.
• A 221° 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: 139°
• 30°
• 45°
• 60°
• 90°
• 120°
• 135°
• 180°