242 Degree Angle

A 242° angle is reflex because it measures between 180° and 360°. It is the "outside" of a 118° angle: together they make a full 360° circle.

242° is 121/180 of a full circle, or 121π/90 radians. If you face north and turn 242° clockwise, you end up facing between SW and WSW (closest to west-southwest (WSW)).

242° angle facts

Trigonometric values of 242°

242° on a protractor

How to draw a 242° angle with a protractor

1. Subtract from 360°: 360° − 242° = 118°. 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 118°.
4. Join the vertex to the dot. The inside angle is 118°; the outside angle, going the long way around, is 242°. Draw the angle arc on the outside and label it 242°.
5. With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 242° directly.

Drawing it a 242° angle without a protractor (rise and run method)

1. 242° = 180° − 62°. Draw a straight line, pick a vertex on it, and build a 62° angle on one side as follows; the angle on the other side of the new line is 118°.
2. Draw a straight baseline and measure 5.32 inches (about 5 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 62°, because tan 62° ≈ 1.8807.
5. That gives you 118°. The outside (reflex) angle is 242°.

Where you see 242° angles

• The Earth turns 242° on its axis in about 16 h 8 min.
• A 242° 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: 118°
• Half: 121°
• 30°
• 45°
• 60°
• 90°
• 120°
• 135°
• 180°