Obtuse Angle Study Guide

1. Definition of Obtuse Angle: An obtuse angle is any angle that measures between 90 and 180 degrees. It is wider than a right angle (90 degrees) but not a straight angle (180 degrees).
2. Identifying Obtuse Angles:
   • Obtuse angles can be identified by measuring the angle with a protractor. If the measure falls between 90 and 180 degrees, it is an obtuse angle.
   • Another way to identify obtuse angles is to visually compare the angle with a right angle (90 degrees). If the angle is wider than a right angle, it is obtuse.
3. Examples of Obtuse Angles:
   • An angle measuring 100 degrees is an obtuse angle.
   • An angle measuring 150 degrees is also an obtuse angle.
   • However, an angle measuring 90 degrees or less is not obtuse.
4. Properties of Obtuse Angles:
   • The sum of an obtuse angle and an acute angle is greater than 180 degrees.
   • The complement of an obtuse angle is an acute angle.
   • The supplement of an obtuse angle is an acute angle.
5. Practice Problems:
   1. Identify whether the following angles are obtuse or not:
      • Angle A: 120 degrees
      • Angle B: 45 degrees
      • Angle C: 160 degrees
   2. Calculate the complement and supplement of the following obtuse angles:
      • Angle X: 110 degrees
      • Angle Y: 135 degrees