Geometry Review: Angles of Polygons and Quadrilaterals

Vocabulary and formulas covering polygon angle sums and the specific properties of quadrilaterals based on Geometry Packet #5.

Sum of Exterior Angles (All Polygons)

The sum of the exterior angles of any polygon is always $360^\circ$.

Sum of Interior Angles (All Polygons)

The formula to find the total measure of all interior angles in an $n$-sided polygon is $180(n-2)$.

Each Interior Angle (Regular Polygons)

The measure of a single interior angle in a regular polygon is calculated using the formula $\frac{180(n-2)}{n}$.

Each Exterior Angle (Regular Polygons)

The measure of a single exterior angle in a regular polygon is calculated using the formula $\frac{360}{n}$.

Parallelogram Properties

A quadrilateral where opposite sides are parallel and congruent, diagonals bisect each other, opposite angles are congruent, and consecutive angles are supplementary.

Rectangle Properties

A quadrilateral that shares all parallelogram properties and also has congruent diagonals.

Rhombus Properties

A quadrilateral that shares all parallelogram properties and also has perpendicular diagonals and diagonals that bisect opposite angles.

Square Properties

A quadrilateral that possesses all the properties of a parallelogram, rectangle, and rhombus.

Consecutive Angles

In parallelograms, rectangles, rhombi, and squares, these angles are supplementary ($\text{Sum} = 180^\circ$).

Diagonals of a Rectangle

Unlike a general parallelogram, the diagonals of this specific quadrilateral must be congruent.

Diagonals of a Rhombus

These diagonals are perpendicular and bisect opposite angles, in addition to bisecting each other.