2. # of sides # of triangles Sum of measures of interior angles 31 1(180)=180 42 2(180)=360 5 33(180)=540 644(180)=720 n n-2(n-2) 180

3. If a convex polygon has n sides, then the sum of the measure of the interior angles is (n – 2)(180°)

4. If a regular convex polygon has n sides, then the measure of one of the interior angles is

5. Ex. 1 Use a regular 15-gon to answer the questions. A)Find the sum of the measures of the interior angles. B)Find the measure of ONE interior angle 2340° 156°

6. Ex: 2 Find the value of x in the polygon 130 126 143 100 117 x 126 + 130 + 117 + 143 + 100 + x = 720 616 + x = 720 x = 104

7. Ex: 3 The measure of each interior angle is 150°, how many sides does the regular polygon have? One interior angle A regular dodecagon

8. Two more important terms Exterior Angles Interior Angles

9. The sum of the measures of the exterior angles of a convex polygon, one at each vertex, is 360°. 1 2 3 4 5

10. 1 3 2

11. 1 3 2 4

12. The measure of each exterior angle of a regular polygon is

13. Ex. 4 Find the measure of ONE exterior angle of a regular 20-gon. 18°

14. Ex. 5 Find the measure of ONE exterior angle of a regular heptagon. 51.4°

15. Ex. 6 The sum of the measures of five interior angles of a hexagon is 625. What is the measure of the sixth angle? 95°