Geometry - Types of Angles and Measurement

An angle is formed when two rays originate from a common endpoint called the vertex. The rays are known as the arms of the angle. For example, in $\angle ABC$, point $B$ is the vertex where rays $BA$ and $BC$ meet.

Acute angles are those that measure more than $0^{\circ}$ but less than $90^{\circ}$. Visually, these angles appear 'sharp' or narrow, resembling the tip of a needle or the letter 'V'.

A right angle measures exactly $90^{\circ}$. It forms a perfect 'L' shape, like the corner of a square or a book. In geometry diagrams, a right angle is often marked with a small square at the vertex instead of a curved arc.

Obtuse angles measure more than $90^{\circ}$ but less than $180^{\circ}$. They look wide and spread out, similar to a wide-open door or a hand fan that is opened past the halfway point.

A straight angle measures exactly $180^{\circ}$. It looks like a perfectly flat, straight line. The vertex is a point on the line, and the two arms extend in opposite directions from that point.

Reflex angles are those that measure more than $180^{\circ}$ and less than $360^{\circ}$. Visually, these represent the 'outer' part of an angle, looking like a large rotation that bends backwards beyond a straight line.

A complete angle (or full rotation) measures exactly $360^{\circ}$. It represents a full circle where the ray rotates all the way back to its starting position, appearing as a single line with a circle around the vertex.

Angles are measured using an instrument called a protractor in units called degrees ($^{\circ}$). When measuring, the center of the protractor must be placed exactly on the vertex, and the zero-line must align with one arm of the angle.