Types of Angles — Definition, Formula & Examples
Types of angles are the categories used to classify angles based on their degree measure. The six main types are acute (less than 90°), right (exactly 90°), obtuse (between 90° and 180°), straight (exactly 180°), reflex (between 180° and 360°), and full (exactly 360°).
An angle is classified by the measure of its opening between two rays sharing a common endpoint (vertex). Angles are partitioned into distinct types according to their degree measure: acute if , right if , obtuse if , straight if , reflex if , and full rotation if .
How It Works
To classify an angle, measure it with a protractor or calculate it from given information, then compare the result to the degree ranges. If the measure is less than 90°, the angle is acute. If it equals exactly 90°, it is a right angle, often marked with a small square at the vertex. Measures between 90° and 180° make the angle obtuse, while exactly 180° gives a straight angle that looks like a flat line. Any angle larger than 180° but less than 360° is called a reflex angle. Knowing these categories helps you describe shapes, solve geometry problems, and communicate about angles quickly.
Worked Example
Problem: Classify each angle: 35°, 90°, 128°, and 210°.
Step 1: Check 35°. Since 0° < 35° < 90°, this is an acute angle.
Step 2: Check 90°. This equals exactly 90°, so it is a right angle.
Step 3: Check 128°. Since 90° < 128° < 180°, this is an obtuse angle.
Step 4: Check 210°. Since 180° < 210° < 360°, this is a reflex angle.
Answer: 35° is acute, 90° is right, 128° is obtuse, and 210° is reflex.
Another Example
Problem: A triangle has angles measuring 60°, 85°, and 35°. Classify each angle and determine what type of triangle this is based on its angles.
Step 1: Classify each angle individually. All three measures (60°, 85°, 35°) are less than 90°.
Step 2: Since every angle is acute, all three are acute angles.
Step 3: A triangle where all angles are acute is called an acute triangle. If even one angle had been greater than 90°, the triangle would be obtuse instead.
Answer: All three angles are acute, so this is an acute triangle.
Visualization
Why It Matters
Classifying angles is one of the first skills taught in elementary and middle-school geometry, and it forms the basis for understanding triangles, quadrilaterals, and other polygons. Architects and engineers use angle types daily — for instance, right angles ensure walls are perpendicular to floors. Knowing the categories also prepares you for topics like complementary and supplementary angle pairs in later courses.
Common Mistakes
Mistake: Confusing obtuse and reflex angles, especially when an angle looks 'big.'
Correction: Obtuse angles measure between 90° and 180°. Reflex angles are larger than 180°. Always check the actual degree measure rather than guessing from appearance.
Mistake: Thinking a right angle must look upright or vertical.
Correction: A right angle is any 90° angle regardless of its orientation. Look for the small square symbol at the vertex, which marks it as 90° no matter how the figure is rotated.