 # Polygon – Shape with many angles; each segment (side) must intersect exactly 2 other segments.

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Polygon – Shape with many angles; each segment (side) must intersect exactly 2 other segments.

Why is this not a polygon? This shape is not formed by a series of segments.

Convex Polygon such that no line connecting two sides falls in the exterior of the polygon.

Why is this nonconvex? Nonconvex A line can be drawn outside the shape. AKA: Concave

Decagon Triangle Quadrilateral Pentagon Octagon 9-gon (Nonagon) n-gon # of Sides 3 4 5 6 7 8 9 10 n Name of Polygon Hexagon 7-gon (Heptagon)

Diagonal A segment that connects two nonconsecutive vertices of a polygon. Connecting two consecutive vertices would create a side of the polygon.

Pentagon A pentagon has five diagonals.

Number of Diagonals in a Polygon

180° Quadrilateral Interior Angles Examples: Sum of Interior Angles: 360°

180° Pentagon Interior Angles Examples: Sum of Interior Angles: 540°

Sum of Interior Angles of a Polygon Based on the number of triangles that can be created within the polygon. Formula

115° 100° 115° 110° 100° 65° 80° 65° 70° 80° Sum of Exterior Angles Exterior Angles Example 360°

Sum of Exterior Angles of a Polygon The sum of the measures of the exterior angles of any convex polygon is 360°.

Regular Polygon – A polygon with that is both equilateral and equiangular. 60°

Irregular Polygon – A polygon with unequal angle measurements or sides of unequal lengths. 120° 60° 120°

Example 1: A polygon has four sides. What is the name of the polygon? What is the sum of the interior angles? What is the sum of the exterior angles? How many diagonals can be drawn? Quadrilateral 360° 2

Example 2: The sum of the interior angles of this polygon is 1440. How many sides does this polygon have? What is the name of the polygon? How many diagonals can be drawn? 10 Decagon 35

Example 3: Fourteen diagonals can be drawn in this polygon. How many sides does this polygon have? What is the name of the polygon? What is the sum of the interior angles? What is the sum of the exterior angles? 7 Heptagon, 7-gon 900 360

Example 4: Each exterior angle of this regular polygon is 60°. What is the sum of the exterior angles? How many sides does this polygon have? How many diagonals can be drawn? 360 6 9

NAME SUM OF INTERIOR ANGLES SUM OF EXTERIOR ANGLES MEASURE OF INT. ANGLE (IF REGULAR) NUMBER OF SIDES 20 4 5 6 7 8 9 10 n 360 180 360 540 720 900 1080 1260 1440 180(n-2) 60 90 108 120 135 144 140 Triangle Quadrilateral Pentagon Octagon Nonagon Decagon n-gon NUMBER OF DIAGONALS 0 2 5 9 14 3 27 35 Hexagon Heptagon

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