7. Polygons can be identified by the number of their sides. 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 measure and all the sides have the same length. Polygons and Angles L E S S O N 8 6 . Pentagon Hexagon Heptagon Octagon 12 - gon 5 sides 6 sides 7 sides 8 sides 12 sides
8. 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 measure and all the sides have the same length. Polygons and Angles L E S S O N 8 6 . Polygons Regular Polygons Not Polygons
9. Identifying Figures Is the figure a polygon, a regular polygon, or not a polygon ? Explain. Not a polygon. The figure does not have line segments as sides. EXAMPLE 1 Polygons and Angles L E S S O N 8 6 .
10. Identifying Figures Is the figure a polygon, a regular polygon, or not a polygon ? Explain. Not a polygon. The figure does not have line segments as sides. Regular polygon. Its angles have equal measures, and its sides have equal lengths. EXAMPLE 1 Polygons and Angles L E S S O N 8 4 .
11. Sum of all angle measures in an n - gon: ( n – 2) • 180º Angle Measures in a Polygon In the activity, you used triangles to find the sum of the angle measures in polygons. In a regular polygon, the measure of one angle is the sum of the angle measures divided by the number of sides. n = number of sides of the polygon NOTE BOOK Polygons and Angles L E S S O N 8 6 . Measure of one angle in a regular n -gon: ( n – 2) • 180º n
12. Finding an Angle Measure Find the measure of one angle in a regular octagon. = 135º Substitute 8 for n . Simplify numerator. Divide. ANSWER The measure of one angle in a regular octagon is 135º . A regular octagon has 8 sides, so use n = 8 . 8 8 EXAMPLE 2 Polygons and Angles L E S S O N 8 6 . ( n – 2) • 180º n = ( n – 2) • 180º n = 1080º 8
13. You can use triangles to find the sum of the angle measures in other figures. Look at the table. We will divide each figure into triangles by drawing as many diagonal lines as we can that begin at the point marked. Polygons and Angles 5 2 3 540º 6 3 4 720º 8 5 6 1080º 4 1 2 360º Activity Shape Quadrilateral Pentagon Hexagon Octagon Number of Sides Number of Diagonal Lines Number of Triangles Formed Sum of Angle Measures L E S S O N 8 6 . . . . .
