Reflex Angle

A reflex angle is an angle that is greater than 180 degrees and less than 360 degrees. It is formed when one arm of the angle is rotated beyond a straight line (180 degrees) but less than a full rotation (360 degrees).

Properties of Reflex Angles:

• A reflex angle measures between 180 degrees and 360 degrees.
• The sum of a reflex angle and its corresponding acute angle (less than 90 degrees) is 360 degrees.
• Reflex angles are commonly found in shapes such as polygons with more than four sides.

Examples of Reflex Angles:

Here are some examples of reflex angles:

1. A circle has a central angle of 360 degrees, so any angle greater than 180 degrees but less than 360 degrees is a reflex angle.
2. In a pentagon (a five-sided polygon), the angles formed by connecting any two non-adjacent vertices will be reflex angles.
3. Angles formed by the hands of a clock when the time is between 6:00 and 12:00 are reflex angles.

How to Measure Reflex Angles:

To measure a reflex angle, you can use a protractor. Place the center of the protractor at the vertex of the angle, align one side of the angle with the zero line of the protractor, and then read the measurement where the other side of the angle intersects the protractor scale.

Practice Questions:

1. What is the measure of the reflex angle formed by the hands of a clock when the time is 9:45?
2. In a hexagon, if one of the reflex angles measures 240 degrees, what is the measure of its corresponding acute angle?
3. Draw and measure a reflex angle that measures 220 degrees using a protractor.