Classifying Triangles by Angles

Triangles can be sorted into three groups based on the size of their angles: acute, right, or obtuse.

Reading is good — doing is better. Practice Classifying Triangles by Angles as an interactive lesson.

Definition

Every triangle has three angles that add up to 180 degrees. We can classify, or sort, a triangle by looking at its largest angle. If all three angles are less than 90 degrees, it is an acute triangle. If one angle is exactly 90 degrees, it is a right triangle. If one angle is greater than 90 degrees, it is an obtuse triangle.

Remember the rule

Check the biggest angle: ALL sharp (under 90°) = Acute | ONE square corner (exactly 90°) = Right | ONE wide angle (over 90°) = Obtuse

Key words

Triangle: A flat shape with exactly 3 straight sides and 3 angles.
Angle: The amount of turn or opening between two sides that meet at a point, measured in degrees.
Degree: The unit we use to measure how big or small an angle is. A full circle has 360 degrees.
Acute angle: An angle that measures less than 90 degrees — it looks like a sharp, pointy opening.
Right angle: An angle that measures exactly 90 degrees — it looks like the corner of a square or a piece of paper.
Obtuse angle: An angle that measures more than 90 degrees but less than 180 degrees — it looks wide and open.
Acute triangle: A triangle where ALL three angles are less than 90 degrees.
Obtuse triangle: A triangle where ONE angle is greater than 90 degrees.

Worked examples

A triangle has angles of 60°, 60°, and 60°. What type is it?

→ Acute triangle. All three angles are less than 90°, so it is acute. · A triangle with three equal angles is called equilateral — it is always acute.

A triangle has angles of 90°, 45°, and 45°. What type is it?

→ Right triangle. One angle is exactly 90°, so it is a right triangle. · You can spot a right angle by the small square symbol drawn in the corner.

A triangle has angles of 120°, 35°, and 25°. What type is it?

→ Obtuse triangle. The 120° angle is greater than 90°, so it is obtuse. · A triangle can only ever have ONE obtuse angle because three angles must total 180°.

A triangle has angles of 80°, 60°, and 40°. What type is it?

→ Acute triangle. All three angles (80°, 60°, 40°) are less than 90°, so it is acute.

A triangle has angles of 90°, 30°, and 60°. What type is it?

→ Right triangle. The 90° angle makes it a right triangle.

Can a triangle have two obtuse angles, say 100° and 95°?

→ No. 100° + 95° = 195°, which is already more than 180°. A triangle's three angles must add up to exactly 180°, so two obtuse angles are impossible. · This is a great way to check your work — always add the three angles to make sure they equal 180°.

Common mistakes

Calling a triangle 'right' just because it looks like it has a right angle without checking that it is exactly 90°.
Forgetting that ALL three angles must be less than 90° for an acute triangle — if even one is 90° or more, it is not acute.
Thinking a triangle can have more than one right angle or more than one obtuse angle — it cannot, because the angles must total 180°.
Confusing an acute angle (a sharp angle in any shape) with an acute triangle (a specific triangle where every angle is acute).
Not adding the three angles to verify they sum to 180°, which is the best way to catch mistakes.

FAQs

Can a triangle be both right and obtuse?

No. A triangle can only belong to one group. If it has a 90° angle it is right; if it has an angle over 90° it is obtuse. It cannot have both because the angles must add up to 180°.

How do I know if an angle is exactly 90° when I look at a triangle?

Look for a small square drawn in the corner of the angle. That symbol always means exactly 90°. You can also use the corner of a piece of paper to check.

Why do all three angles always add up to 180°?

That is a rule that is true for every triangle, no matter the size or shape. You can tear off the three corners of any paper triangle and line them up — they will always form a straight line, which is 180°.

What if I only know two of the three angles?

Add the two angles you know, then subtract from 180°. The answer is the missing angle. For example, if two angles are 70° and 50°, the third is 180° − 70° − 50° = 60°.

Is an equilateral triangle (all sides equal) always the same type?

Yes! An equilateral triangle always has three 60° angles, so it is always an acute triangle.

My triangle looks pointy — does that mean it is acute?

Not necessarily. A triangle can look pointy and still be obtuse if one angle opens wide (over 90°) while the other two are very small. Always measure or check the angles, do not just guess by looking.

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