Polygons and Angle Relationships

Vocabulary and formulas related to the properties, parts, and classification of polygons, including interior and exterior angle calculations.

Polygon

A closed plane figure where sides meet only at their endpoint; the term originates from the Greek words "poly" (many) and "gonia" (angles).

Vertex

The point where $2$ sides of a polygon meet.

Side

The boundary of the polygon.

Angle

A feature located at the vertices of a polygon.

Irregular Polygon

A polygon that is neither equilateral nor equiangular.

Linear Pair

Adjacent angles that have opposite rays and are supplementary at the same time.

Vertical angles

Angles formed by two intersecting lines that are opposite to each other and are congruent.

Adjacent Angles

Angles that are side by side and have a common side and vertex.

Sum of interior angles formula

$S = (n - 2) \times 180^{\circ}$, where $S$ is the sum and $n$ is the number of sides.

Sum of the exterior angles

The sum of the exterior angles of any convex polygon is always equal to a complete turn, which measures $360^{\circ}$.

Interior Angle of a Regular Polygon formula

The formula used to find the measure of each interior angle in a regular polygon: $m(\text{Int.} \angle) = \frac{(n - 2) \times 180^{\circ}}{n}$.

Number of sides floor formula

A method to find the number of sides using the exterior angle: $n = 360^{\circ} \div (180^{\circ} - \text{Int.} \angle)$.

Triangle

A polygon with $3$ sides and a sum of interior angles equal to $180^{\circ}$.

Quadrilateral

A polygon with $4$ sides and a sum of interior angles equal to $360^{\circ}$.

Pentagon

A polygon with $5$ sides and a sum of interior angles equal to $540^{\circ}$.

Hexagon

A polygon with $6$ sides and a sum of interior angles equal to $720^{\circ}$.

Heptagon

A polygon with $7$ sides and a sum of interior angles equal to $900^{\circ}$.

Octagon

A polygon with $8$ sides and a sum of interior angles equal to $1080^{\circ}$.

n-gon

A polygon with $n$ sides, having $n-2$ triangles and a sum of interior angles equal to $(n - 2) \times 180^{\circ}$.