Which of the following angular inequalities defines an obtuse angle?

Step 1: Analyze the question We need the inequality that describes an obtuse angle.

Step 2: The concept Angles are classified by size:

• Acute angle: greater than 0° and less than 90°
• Right angle: exactly 90°
• Obtuse angle: greater than 90° but less than 180°
• Straight angle: exactly 180°
• Reflex angle: greater than 180° but less than 360°

So an obtuse angle satisfies 90° < x < 180°. Both ends are strict (not included), because 90° is a right angle and 180° is a straight angle, and neither is obtuse.

Step 3: Check each option

• A. 0° < x < 90° is the range for an acute angle.
• B. 0° ≤ x > 180° is badly written and contradictory. It describes no sensible range, and it includes 0°.
• C. 90° < x < 180° is exactly the obtuse range. ✔
• D. 90° ≤ x < 180° includes 90°, which is a right angle, not obtuse.
• E. 90° > x < 180° is badly formed. It says x is less than 90° and also less than 180°, which just means x < 90° (acute).

Step 4: Answer

Exam tip: Remember "obtuse" as "bigger than a right angle, but not yet straight". Always check whether the boundary values (90° and 180°) are included. For obtuse angles they are not, so look for the strict "<" signs on both sides.