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# Definitions

## Individual Angles

Mathematicians categorize angles based on their measures:

An angle is acute if its measure is strictly less than 90°.

An angle is a right angle if its measure is exactly 90°.

An angle is obtuse if its measure is strictly greater than 90°.

Some textbooks call an angle whose measure is 180° a straight angle. Essentially this is a line so some books don't consider it an angle at all.

Take a look at some examples.

 an acute angle(m < 90°) a right angle(m = 90°) an obtuse angle(90° < m < 180°) a straightangle(m = 180°)

Note the little box in the right angle. Right angles are sort of special and come up a lot so there's a special way to let you know that's what you're looking at.

## Pairs of Angles

Mathematicians also classify pairs of angles based on their angle measures and their arrangement.

 Two angles are complementary if the sum of their angle measures is 90°. The angles in the picture to the right are complementary because 30° + 60° = 90°. Two angles are supplementary if the sum of their angle measures is 180°. The angles in the picture to the right are supplementary because 60° + 120° = 180°. Two angles are adjacent if they have a common side and no interior points in common. Another way of saying "have a common side" would be "they have the same vertex". In the diagram ∠ABD and ∠DBC are adjacent angles but ∠DBC and ∠ABC are not because they have interior points in common (e.g. E). Vertical angles are the non-adjacent angles formed by two intersecting lines. In the diagram to the left angles 1 and 3 are vertical angles but angles 1 and 4 are not because they're adjacent. (Angles 2 and 4 are vertical also - vertical angles always come in sets of two.) Two angles form a linear pair if they are adjacent and supplementary.