Problem: A triangle has angles measuring 25°, 35°, and 120°. Which angle is obtuse?
Step 1: Check each angle against the definition: an obtuse angle must satisfy 90° < measure < 180°.
Step 2: 25° is less than 90°, so it is acute. 35° is less than 90°, so it is also acute.
Step 3: 120° is greater than 90° and less than 180°, so it meets the definition.
90°<120°<180°
Answer: The 120° angle is the obtuse angle.
Why It Matters
Obtuse angles appear throughout geometry and real life — the wide angle of a reclining chair or the slant of a roof can both be obtuse. Recognizing them is essential for classifying triangles: a triangle with one obtuse angle is called an obtuse triangle, which affects how you calculate its area and apply trigonometric rules.
Common Mistakes
Mistake: Confusing an obtuse angle with a reflex angle.
Correction: An obtuse angle is strictly between 90° and 180°. A reflex angle is between 180° and 360°. If the measure equals or exceeds 180°, it is not obtuse.
Related Terms
Angle — General concept that obtuse angle belongs to
Mathwords