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6-1 Angles of Polygons N#____ ____/____/____

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6-1 Angles of PolygonsN#____ ____/____/____

SLG : Students will be able to find and use the sum of the measures of the interior angles of a polygon, and find and use the sum of the measures of the exterior angles of a polygon.

Convex

Concave

Diagonal: a segment that connects any two non consecutive vertices

A

B

D

C

If we draw all possible diagonals from one vertex of a convex polygon, it divides the polygon into triangles.

The sum of the interior angles of a triangle always equals 180.

180

180

180

180

180

180

180

180

180

180

Interior

Angle =

Sum

E1 What is the sum of the interior angles of a nonagon?

E2 A convex polygon has an interior angle sum of 1620, how many sides does it have?

Regular Polygon: a convex polygon where all the sides and angles are congruent

E3 A regular polygon has an interior angle of 135 degrees. How many sides does it have?

4x

4x

E4 Find the value of x.

2x+20

3x-10

3x-20

2x+10

Exterior Angle of a Polygon: made of one side of a polygon and extending another side

90

72

120

90

72

108

60

108

108

90

72

60

60

120

108

72

108

90

120

72

Exterior

Angle =

Sum

E5 Find the sum of the exterior angles of a regular convex octagon.

Exterior angle sum of any convex polygon is 360

If the sum is always 360, then to find one exterior angle in a regular polygon you would divide 360 by the number of sides.

E6 Find the measure of one exterior angle in a regular pentagon.

The sum of one exterior angle of a convex polygon is 360° ÷ n where n is the number of sides of the polygon

SWS 6-1