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Aim: How do we find angle measures in polygons? A polygon is a closed figure whose sides are line segments that intersect only at their endpoints. In a regular polygon, all the angles have the same measures and all the sides have the same length. Polygons can be indentified by the number of their sides Regular Polygons Polygons Not Polygons

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Aim: How do we find angle measures in polygons? Practice- Is the shape a polygon, a regular polygon or not a polygon? 1. Not a Polygon – The sides are not line segments Regular Polygon – All the sides and angles have the same measure. Polygon – All the sides are line segments.

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Aim: How do we find angle measures in polygons?

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A vertex is a point where two sides meet. The interior angles of a polygon are the angles inside the polygon. A diagonal of a polygon is a line segment that joins two nonconsecutive vertices. What is the sum of the measures of the interior angles of a quadrilateral? Vertex Interior Angles Diagonal Since the quadrilateral is made up of 2 triangles, the sum the angles is 2(180 o ) = 360 o

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Aim: How do we find angle measures in polygons? You can use triangles to find these sum of the angle measures in other figures. ShapeQuadrilateralPentagonHexagonHeptagon Number of Sides Number of Diagonals from one vertex Number of Triangles Formed Sum of Angle Measures Sum of angle measures in an n-gon = (n-2) (180 o )=360 o (180 o )=540 o (180 o )=720 o (180 o )= 900 o 13-gon n-gon (180 o ) =1980 o n n-2 (n-2)180 o

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Aim: How do we find angle measures in polygons? 1. Find the sum of the measures of the interior angles of octagon. An octagon has 8 sides, so n=8. (n-2)180 (8-2)180 (6)180 1,080 o 2. Find the sum of the measures of the interior angles of an 11-gon. A 11-gon has 11 sides, so n=11. (n-2)180 (11-2)180 (9)180 1,620 o Sum of an angle measures in an n-gon = (n-2) 180

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Aim: How do we find angle measures in polygons? Find the sum of the measures of the interior angles in the polygon. 3) 14-gon 4) 17-gon 5) 19-gon

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Aim: How do we find angle measures in polygons? Remember, in a regular polygon, all the angles have the same measure. Hexagon Regular Hexagon 6) Find the measure of one angle in a regular hexagon. (n-2)180 (6-2)180 (4) o 720 ÷ 6 = 120 o 120 o

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Aim: How do we find angle measures in polygons? Measure of one angle in a regular n-gon = (n-2) 180. n Measure of one angle in a regular n-gon = (n-2) 180. n Sum of an angle measures in an n-gon = (n-2) 180 7) Find the measure of one angle in a regular octagon. A regular octagon has 8 sides, so n=8. = (n-2)180 n = (8-2)180 8 = (6)180 8 = = 135 o One angle in a regular octagon is 135 o. 8) Find the measure of one angle in a regular 14-gon. Round to the nearest tenth of a degree. A regular 14-gon has 14 sides, so n=14. = (n-2)180 n = (14-2) = (12) = = o One angle in a regular 14-gon is o.

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Aim: How do we find angle measures in polygons? Find the measure of one angle in the polygon. 9) Regular 12-gon 10) Regular 16-gon 11) Regular 20-gon

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Aim: How do we find angle measures in polygons? Indentify the Polygon 12) The sum of the measures of the interior angles in a polygon is 1,440 o. What type of polygon is it? 1440 = (n-2) = 180n = 180n = n Sum of an angle measures in an n-gon = (n-2) 180 A polygon interior angles that has a sum of 1440 o is a decagon.

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Aim: How do we find angle measures in polygons? Practice- Identify the polygon whose interior angles have the following sum. 13) 1800 o 14) 1260 o 15) 3420 o

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Aim: How do we find angle measures in polygons? Find the value of x. 16) 115 o xoxo 98 o xoxo 140 o 175 o 150 o (n-2)180 (6-2)180 (4)180 =720 o 720 = x 720 = 563 +x 157 = x 17)

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Aim: How do we find angle measures in polygons? Find the value of x. 18) 19)

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Aim: How do we find angle measures in polygons? 20)

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Aim: How do we find angle measures in polygons? 20) 21) 22)

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Aim: How do we find angle measures in polygons? 23) 24) 25)

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