2.4 - Angles Properties in a Quadrilateral Name:______________________ Definition of a Quadrilateral: _________________________________________________________________________________________________________________ Sum of all interior angles of a quadrilateral is ALWAYS equal to 360°. Special types of a quadrilateral:

Property Trapezoid Parallelogram Rhombus Rectangle Square

Opposite sides are parallel

Opposite sides are congruent

All sides are congruent

All angles are congruent

Opposite angles are congruent

All angles are right angles

Diagonals are congruent

Diagonals bisect each other

Diagonals are perpendicular

Each diagonal bisects two angles

2.4 - Angle Properties in Polygons A convex polygon is any polygon in which each interior angle measure less than 180°. A concave polygon is a polygon in which one or more interior angle measures more than 180°

Example 1. Determine if each polygon is concave or convex

a) b) Determine Properties of Angles in Polygons Example 2. Use the following table to determine how to find the sum of the interior angles of a polygon from the number of sides.

Example 3: Calculate the sum of the measure of interior angles of a polygon with:

a) 9 sides b) 12 sides c) 15 sides

Example 4. Determine the number of sides of a polygon whose interior angle sum equals: a) 4140° b) 720°

c) 1260° d) 2880°

A regular polygon is a polygon with all sides equal and all angles equal.

For a regular polygon with n sides, the measure of each interior angle is 180°(𝑛−2)

𝑛

Example 5. What is the measure of each interior angles of a:a) Regular pentagon?

b) Regular decagon?

Example 6. Determine the number of sides of a regular polygon whose interior angle measures:

a) 170° b) 156°

The exterior angle of an n-sided regular polygon measures 360°

𝑛.

The sum of the measures of the exterior angles of an n-sided regular polygon is 360° Example 7: Determine the measure of each exterior angle of a regular pentagon Example 8: Determine the number of sides of a regular polygon whose exterior angle measures

a) 15° b) 40° c) 1°