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**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 Not Polygons Polygons

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**Practice- Is the shape a polygon, a regular polygon or not a polygon?**

1. 2. 3. 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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**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. Vertex What is the sum of the measures of the interior angles of a quadrilateral? Interior Angles Since the quadrilateral is made up of 2 triangles, the sum the angles is 2(180o) = 360o Diagonal

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**Sum of angle measures in an n-gon = (n-2) 180**

You can use triangles to find these sum of the angle measures in other figures. Shape Quadrilateral Pentagon Hexagon Heptagon Number of Sides Number of Diagonals from one vertex Number of Triangles Formed Sum of Angle Measures 13-gon n-gon n n-2 (n-2)180o 4 1 2 2(180o)=360o 5 2 3 3(180o)=540o 6 3 4 4(180o)=720o 7 4 5 5(180o)=900o 13 10 11 11(180o) =1980o Sum of angle measures in an n-gon = (n-2) 180

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**Sum of an angle measures in an n-gon = (n-2) 180**

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

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**Find the sum of the measures of the interior angles in the polygon.**

3) 14-gon ) 17-gon ) 19-gon

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**Remember, in a regular polygon, all the angles have the same measure.**

Hexagon 120 o Hexagon 120 o 120 o 6) Find the measure of one angle in a regular hexagon. (n-2)180 (6-2)180 (4)180 720 o 720 ÷ 6 = 120 o

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**Sum of an angle measures in an n-gon = (n-2) 180**

Measure of one angle in a regular n-gon = (n-2) 180. n 8) Find the measure of one angle in a regular 14-gon. Round to the nearest tenth of a degree. 7) Find the measure of one angle in a regular octagon. A regular octagon has 8 sides, so n=8. A regular 14-gon has 14 sides, so n=14. = (n-2)180 n = (n-2)180 n = (8-2)180 8 = (14-2)180 14 = (6)180 8 = (12)180 14 = 1080 8 = 135 o = 2160 14 = o One angle in a regular octagon is 135 o. One angle in a regular 14-gon is o.

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**Find the measure of one angle in the polygon.**

9) Regular 12-gon ) Regular 16-gon ) Regular 20-gon

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**Sum of an angle measures in an n-gon = (n-2) 180**

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? Sum of an angle measures in an n-gon = (n-2) 180 1440 = (n-2)180 1440 = 180n-360 1800 = 180n 10 = n A polygon interior angles that has a sum of 1440o is a decagon.

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**Practice- Identify the polygon whose interior angles have the following sum.**

13) o ) 1260o ) 3420o

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**Find the value of x. 17) 16) 98o xo 140o 175o 150o xo 115o (n-2)180**

(6-2)180 720 = 563 +x (4)180 157 = x =720 o

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Find the value of x. 18) )

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