Obtuse triangle
High School
Definition
A triangle which contains one obtuse angle in its interior angles. In other words, it is a triangle with one angle that is greater than 90°. The sum of the interior angles of an obtuse triangle will equal 360°.
Worked examples
\(\)Triangle with angles \( 110^\circ, 45^\circ, 25^\circ\)
Since \(110^\circ > 90^\circ\), this is an obtuse triangle; the three angles sum to \(180^\circ\).
\(\)Triangle with angles \( 120^\circ, 35^\circ, 25^\circ\)
The \(120^\circ\) angle makes it obtuse; no triangle can have more than one obtuse angle.
Common mistakes
- An obtuse triangle's angles sum to \(360^\circ\) → An obtuse triangle's angles sum to \(180^\circ\) All triangles have interior angles summing to \(180^\circ\), not \(360^\circ\).
- A triangle with angles \(95^\circ, 50^\circ, 45^\circ\) is not obtuse because \(95^\circ\) is close to \(90^\circ\) → Any angle greater than \(90^\circ\) makes it obtuse Obtuse means strictly greater than \(90^\circ\); \(95^\circ\) qualifies.
- A triangle can have two obtuse angles → A triangle can have at most one obtuse angle Two obtuse angles would sum to more than \(180^\circ\), impossible in a triangle.
Where you'll use it next
You'll classify triangles by angles when studying trigonometry, the Law of Cosines for obtuse cases, and triangle congruence and similarity proofs in geometry.
Found in 1 StudyPug lesson
Mastering Triangle Classification: Your Key to Geometry Success
10th Grade10thGeometry
Unlock the world of geometry by mastering triangle classification. Learn to identify and understand various triangle types, their properties, and real-world applications. Boost your problem-solving skills today!
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026