6.1: Polygon Angle Theorems Objectives Find and use the measures of interior and exterior angles of polygons. Handbook p. 19

Sum of Interior  Measures Polygon Angle Sum Theorem: 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 # of Sides # of Triangles Sum of Interior  Measures Triangle Quadrilateral Pentagon Hexagon n-gon

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°

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 measures. (n – 2)180° (16 – 2)180° = 2520° Step 2: Find the measure of one interior angle.

Handbook page 19 Interior Angles Exterior Angles Sum of all angles Measure of one if the polygon is REGULAR!

6.1: Polygon Angle Theorems 3. Find the measure of each interior angle of pentagon ABCDE. (5 – 2)180° = 540° 35c + 18c + 32c + 32c + 18c = 540 135c = 540 c = 4 mA = 35(4°) = 140° mB = mE = 18(4°) = 72° mC = mD = 32(4°) = 128°

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?

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°.

5. Find the measure of each exterior angle of a regular 20-gon. A 20-gon has 20 sides and 20 vertices. Sum of ext. s = 360°. Measure of one ext.  = The measure of each exterior angle of a regular 20-gon is 18°.

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!

6. Find the value of b in polygon FGHJKL. 15b° + 18b° + 33b° + 16b° + 10b° + 28b° = 360° 120b = 360 b = 3

7. Name the 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.