Properties and Attributes of Polygons

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Presentation transcript:

Properties and Attributes of Polygons 6.1 Properties and Attributes of Polygons

Polygon Vocab POLYGON: Diagonal: Concave Polygons: Convex polygons: Regular polygon:

Name the polygon by how many sides it has.

Sum of interior angles (& each angle!)

Sum interior angles = (n – 2)•180º Ex 1: Find the sum of the measures of interior angles of the convex polygon: (*Think – how many triangles will it divide into?) a) hexagon b) decagon c) 13-gon b) 121-gon

6-1: Angles Measures in Polygons 4/15/2017 Ex 2: Find the value of x 3x-2 3x 3x+4 4x-5 4x x+3 Find sum of all interior angles 2) Set up equation Ex 3: The sum of the interior angles = 2700º. Find the # of sides. M217 - Denna

Ex 4: Find the number of sides (n) of the convex regular polygon if… (Formula to find the sum of angles: ___________________) ONE interior angle = 160º

Exterior Angles of a polygon: Find each exterior angle 1 = 2 = 3 = 4 = 5 = Sum =

Ex 6: Find the value of x

For ALL Convex Polygons Sum of exterior angles Sum = 360º ONE exterior angle of a regular n-gon is: Exterior  = 360 n

In Summary… Sum interior angles of a convex n-gon is: Sum = (n – 2)180 One interior angle of a regular n-gon is:

Ex 7: Find the measure of each exterior and interior angle if given the # of sides of a regular polygon. 7 sides Exterior Angle Interior Angle 19 sides