1. Do Now Find the measures of the three angles. In ABC , m A = x° , m B = 3 x° , and m C = (4 x – 12) ° . ANSWER 24°, 72°, 84°

2. 8.1 Angle Measures in Polygons

3. If all the  s in a Δ add up to 180 o . Then what about the  s in a quadrilateral and pentagon? 3 * 180 = 540 o How about a hexagon? 4 * 180 = 720 o 2 * 180 = 360 0

4. # of sides # of triangles Sum of measures of interior angles 3 1 1(180)=180 4 2 2(180)=360 5 3 3(180)=540 6 4 4(180)=720 n n-2 (n-2) • 180

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

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

8. 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

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

10. Two more important terms Exterior Angles Interior Angles

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

12. 1 3 2 The sum of the measures of the exterior angles of a convex polygon, one at each vertex, is 360 ° .

13. 1 3 2 4 The sum of the measures of the exterior angles of a convex polygon, one at each vertex, is 360 ° .

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

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

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

17. 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°

18. Let’s practice! 8.1 Worksheet

19. Look on the bottom of the Worksheet Homework