# 6-1 Properties and Attributes of Polygons 6.1: Polygon 6-1 Properties and Attributes of Polygons 6.1: Polygon Angle Theorems Objectives Find and use the measures of interior and exterior angles of polygons. Handbook p. 19 Holt Geometry Polygon Angle Sum Theorem: 6-1 Properties and

Attributes of Polygons The sum of the interior angles of a convex polygon is (n 2) ) 180. Draw each diagonal from a single vertex, then complete the chart. Polygon Triangle Quadrilateral Pentagon Hexagon n-gon Holt Geometry # of Sides # of Triangles

Sum of Interior Measures 6-1 Properties and Attributes of Polygons 6.1: Polygon Angle Theorems 1. Find the sum of the interior angle measures of a convex heptagon. (n 2) )180 (7 2) )180 900 Holt Geometry 6-1 Properties and Attributes of Polygons

6.1: Polygon Angle Theorems 2) . Find the measure of each interior angle of a regular 16-gon. Step 1: Find the sum of the interior angle measure (n 2) )180 (16 2) )180 = 2) 52) 0 Step 2: Find the measure of one interior angle. Holt Geometry 6-1 Properties and Attributes of Polygons Handbook page 19

Interior Angles Sum of all angles 180( n 2) Measure of one if the polygon is REGULAR! Holt Geometry 180(n 2) n Exterior Angles 6-1 Properties and Attributes of Polygons

6.1: Polygon Angle Theorems 3. Find the measure of each interior angle of pentagon ABCDE. (5 2) )180 = 540 35c + 18c + 32) c + 32) c + 18c = 540 135c = 540 c=4 mA = 35(4) = 140 mB = mE = 18(4) = 72) mC = mD = 32) (4) = 12) 8 Holt Geometry 6-1 Properties and Attributes of Polygons

6.1: Polygon Angle Theorems 4a. What is the measure of each interior angle of a regular decagon? b. What is the measure of each exterior angle of a regular decagon? c. What is the SUM of all of the exterior angles? Holt Geometry 6-1 Properties and Attributes of Polygons 6.1: Polygon Angle Theorems

In the polygons below, an exterior angle has been measured at each vertex. Notice that in each case, the sum of the exterior angle measures is 360. Holt Geometry 6-1 Properties and Attributes of Polygons 5. Find the measure of each exterior angle of a regular 20-gon. A 2) 0-gon has 2) 0 sides and 2) 0 vertices.

Sum of ext. s = 360. Measure of one ext. = The measure of each exterior angle of a regular 2) 0gon is 18. Holt Geometry 6-1 Properties and Attributes of Polygons Angle measures of a convex polygon with n sides Interior Angles Exterior Angles Sum of all angles Measure of one if the polygon is REGULAR!

Holt Geometry 180(n 2) 360 180(n 2) n 360 n 6. Find the value of b in of Polygons 6-1 Properties

and Attributes polygon FGHJKL. 15b + 18b + 33b + 16b + 10b + 2) 8b = 360 12) 0b = 360 b=3 Holt Geometry 6-1 Properties Attributes of Polygons 7. Name theand convex polygon

whose sum of its interior angle measures is 6840. 8. The exterior angle of a regular polygon is about 27.7. Find the number of its sides and the measure of each interior angle. Holt Geometry