An angle is formed wherever two rays share a common endpoint, called the vertex, and angles are measured in degrees based on the amount of rotation between them. The basic types describe where the angle falls on the 0° to 180° scale. An acute angle measures greater than 0° and less than 90°, with familiar examples including 30°, 45°, and 60°. An obtuse angle measures greater than 90° and less than 180°, such as 120°. A right angle measures exactly 90° and is often marked with a small square at the vertex to distinguish it from other angles. A straight angle measures exactly 180° and forms a flat line, essentially a half-turn.
Angles can also be grouped by how they relate to one another. Complementary angles are two angles whose measures add up to exactly 90°, so a 35° angle and a 55° angle are complementary. Supplementary angles are two angles whose measures add up to exactly 180°, so 110° and 70° form a supplementary pair. When two lines cross, the pairs of opposite angles they create are called vertical angles, and vertical angles are always congruent, meaning they have the same measure. Adjacent angles share a common vertex and a common side but do not overlap; they simply sit next to each other.
Understanding these angle categories is essential because they appear constantly in proofs and calculations. The fact that vertical angles are equal and that adjacent angles on a straight line sum to 180° lets us find unknown angle measures whenever a figure has intersecting or straight lines. Combined with the right angle and the straight angle, these building blocks provide the vocabulary needed to describe everything from simple triangles to the more complex relationships that arise when parallel lines meet a transversal.