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# of sides # of triangles Sum of measures of interior angles 31 1(180)=180 42 2(180)=360 5 33(180)=540 644(180)=720 n n-2(n-2) 180

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If a convex polygon has n sides, then the sum of the measure of the interior angles is (n 2)(180)

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If a regular convex polygon has n sides, then the measure of one of the interior angles is

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Ex. 1 Use a regular 15-gon to answer the questions. A)Find the sum of the measures of the interior angles. B)Find the measure of ONE interior angle 2340 156

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Ex: 2 Find the value of x in the polygon 130 126 143 100 117 x 126 + 130 + 117 + 143 + 100 + x = 720 616 + x = 720 x = 104

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Ex: 3 The measure of each interior angle is 150, how many sides does the regular polygon have? One interior angle A regular dodecagon

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Two more important terms Exterior Angles Interior Angles

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The sum of the measures of the exterior angles of a convex polygon, one at each vertex, is 360. 1 2 3 4 5

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1 3 2

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1 3 2 4

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The measure of each exterior angle of a regular polygon is

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Ex. 4 Find the measure of ONE exterior angle of a regular 20-gon. 18

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Ex. 5 Find the measure of ONE exterior angle of a regular heptagon. 51.4

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Ex. 6 The sum of the measures of five interior angles of a hexagon is 625. What is the measure of the sixth angle? 95

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Lets practice! 11.1 Worksheet

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ss Area of an Equilateral Triangle s 60 30

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Ex: 1 Find the area of an equilateral triangle with 4 ft sides.

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A Circle can be circumscribed around any regular polygon

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VERTICES

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A RADIUS joins the center of the regular polygon with any of the vertices A Central Angle is an angle whose vertex is the center and whose sides are two consecutive radii

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A Regular Hexagon Equal Angles Equal Sides How many equilateral triangles make up a regular Hexagon? What is the area of each triangle? What is the area of the hexagon? s 6 (the area of the triangle)

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4 The area of an equilateral triangle The area of our equilateral triangle in this exampleA = 6.9282 The area of our hexagon in this exampleA = 6 * (6.9282) How many identical equilateral triangles do we have?6 41.569 units 2 What is the area of this regular hexagon?

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An APOTHEM is the distance between the center and a side. (It MUST be perpendicular to the side.)

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How to find the You need to know the apothem and perimeter Area = (1/2)aP or A =.5aP

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Area of a Regular Polygon: A = aP a A =.5 (apothem) (# of sides)(length of each side)

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A Regular Octagon 7 ft

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45 7 3.5 ft 22.5 x 360/8=45

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7 ft Perimeter is 56 feet Apothem is 8.45 feet What is the area? Area =.5 8.45 56 Area = 236.6 ft 2

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11.2 Worksheet Practice B ODDS

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Worksheets EVENS