Obtuse Angles: Which inequality describes an obtuse angle measure?

Obtuse Angles: Which inequality describes an obtuse angle measure?

• A. x < 90
• B. 90 < x < 180
• C. x = 180
• D. x > 180

Answer: (B)

Obtuse angles are larger than a right angle but smaller than a straight angle. Since a right angle is 90 degrees and a straight angle is 180 degrees, an obtuse angle must satisfy 90 < x < 180. This places it between a 90-degree angle and a 180-degree angle. If you used x < 90, it would be acute; if x = 180, it’s a straight angle; if x > 180, it’s a reflex angle.

Obtuse angles are larger than a right angle but smaller than a straight angle. Since a right angle is 90 degrees and a straight angle is 180 degrees, an obtuse angle must satisfy 90 < x < 180. This places it between a 90-degree angle and a 180-degree angle. If you used x < 90, it would be acute; if x = 180, it’s a straight angle; if x > 180, it’s a reflex angle.